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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:67"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="topreal1.html#R1">is_an_arc_of</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="struct_0.html#NM7">Function</a> of <a href="topmetr.html#K5">I[01]</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span><b> such that </b><br/><a NAME="E3:67"/><i><font color="Green">E59</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a>  &amp; <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="topreal1.html#D2">TOPREAL1:def 2</a></i>;<br/>
<a NAME="E4:67"/><i><font color="Green">E60</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> is <a href="pre_topc.html#V5">continuous</a> &amp; <font color="Maroon">c<sub>5</sub></font> is <a href="funct_1.html#V2">one-to-one</a> )
 
<b>by </b><i><a class="txt" href="borsuk_4.html#E3:67"><i><font color="Green">E59</font></i></a>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> the <a href="struct_0.html#U1">carrier</a> of <a href="borsuk_4.html#K1" target="_self">I(01)</a> ;<br/>
<a NAME="E5:67"/><i><font color="Green">E61</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <a href="borsuk_4.html#K1" target="_self">I(01)</a>  <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="topmetr.html#K5">I[01]</a> 
 
<b>by </b><i><a class="ref" href="borsuk_1.html#T35">BORSUK_1:35</a></i>;<br/>
<a NAME="E6:67"/><i><font color="Green">E62</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="topmetr.html#K5">I[01]</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E7:67"/><b>then </b><i><font color="Green">E63</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> the <a href="struct_0.html#U1">carrier</a> of <a href="borsuk_4.html#K1" target="_self">I(01)</a> </span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="borsuk_4.html#K1" target="_self">I(01)</a> 
 
<b>by </b><i><a class="txt" href="borsuk_4.html#E5:67"><i><font color="Green">E61</font></i></a>, <a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <a href="borsuk_4.html#K1" target="_self">I(01)</a>  as   <a href="struct_0.html#NM2">Subset</a> of <a href="topmetr.html#K5">I[01]</a>  <b>by </b><i><a class="ref" href="borsuk_1.html#T35">BORSUK_1:35</a></i>;<br/>
<i><font color="Green">E64</font></i>:  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>5</sub></font> = 
 <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="borsuk_4.html#E3:67"><i><font color="Green">E59</font></i></a>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>
<br/>.= 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>

<br/>.= 
<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="pre_topc.html#T29">PRE_TOPC:29</a></i>
;<br/>
<a NAME="E10:67"/><i><font color="Green">E65</font></i>: 
( 0 <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font> &amp; 1 <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="txt" href="borsuk_4.html#E6:67"><i><font color="Green">E62</font></i></a>, <a class="ref" href="borsuk_1.html#T86">BORSUK_1:86</a></i>;<br/>
<i><font color="Green">E66</font></i>: <font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K10">.:</a> the <a href="struct_0.html#U1">carrier</a> of <a href="borsuk_4.html#K1" target="_self">I(01)</a>  = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K10">.:</a> the <a href="struct_0.html#U1">carrier</a> of <a href="topmetr.html#K5">I[01]</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p2"><a href="domain_1.html#K7">{</a><span class="default">0,1</span><a href="domain_1.html#K7">}</a></span></span>)</span>
<b>by </b><i><a class="txt" href="borsuk_4.html#E4:67"><i><font color="Green">E60</font></i></a>, <a class="ref" href="borsuk_4.html#T58" target="_self">Th58</a>, <a class="ref" href="funct_1.html#T123">FUNCT_1:123</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p2"><a href="domain_1.html#K7">{</a><span class="default">0,1</span><a href="domain_1.html#K7">}</a></span></span>)</span>
<b>by </b><i><a class="txt" href="borsuk_4.html#E6:67"><i><font color="Green">E62</font></i></a>, <a class="txt" href="borsuk_4.html#E9:67"><i><font color="Green">E64</font></i></a>, <a class="ref" href="relat_1.html#T146">RELAT_1:146</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span>
<b>by </b><i><a class="txt" href="borsuk_4.html#E3:67"><i><font color="Green">E59</font></i></a>, <a class="txt" href="borsuk_4.html#E10:67"><i><font color="Green">E65</font></i></a>, <a class="ref" href="funct_1.html#T118">FUNCT_1:118</a></i>
;<br/>
<a NAME="E12:67"/>
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> the <a href="struct_0.html#U1">carrier</a> of <a href="borsuk_4.html#K1" target="_self">I(01)</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K10">.:</a> the <a href="struct_0.html#U1">carrier</a> of <a href="borsuk_4.html#K1" target="_self">I(01)</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T148">RELAT_1:148</a></i>;<br/>
<a NAME="E13:67"/><b>then </b><i><font color="Green">E67</font></i>: 
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> the <a href="struct_0.html#U1">carrier</a> of <a href="borsuk_4.html#K1" target="_self">I(01)</a> </span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="borsuk_4.html#E11:67"><i><font color="Green">E66</font></i></a>, <a class="ref" href="pre_topc.html#T29">PRE_TOPC:29</a></i>;<br/>
<a NAME="E14:67"/><i><font color="Green">E68</font></i>: 
 <a href="borsuk_4.html#K1" target="_self">I(01)</a>  <a href="hidden.html#R1">=</a> <a href="topmetr.html#K5">I[01]</a>  <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="borsuk_4.html#T57" target="_self">Th57</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> the <a href="struct_0.html#U1">carrier</a> of <a href="borsuk_4.html#K1" target="_self">I(01)</a>  as   <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K5">I[01]</a>  <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <b>by </b><i><a class="ref" href="funct_2.html#T38">FUNCT_2:38</a></i>;<br/>
<a NAME="E16:67"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">c<sub>8</sub></font> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="txt" href="borsuk_4.html#E4:67"><i><font color="Green">E60</font></i></a>, <a class="ref" href="topmetr.html#T10">TOPMETR:10</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> the <a href="struct_0.html#U1">carrier</a> of <a href="borsuk_4.html#K1" target="_self">I(01)</a>  as   <a href="struct_0.html#NM7">Function</a> of <a href="borsuk_4.html#K1" target="_self">I(01)</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span></span>)</span></span>)</span> <b>by </b><i><a class="txt" href="borsuk_4.html#E7:67"><i><font color="Green">E63</font></i></a>, <a class="txt" href="borsuk_4.html#E13:67"><i><font color="Green">E67</font></i></a>, <a class="ref" href="funct_2.html#T3">FUNCT_2:3</a></i>;<br/>
<a NAME="E18:67"/><i><font color="Green">E70</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <a href="borsuk_4.html#K1" target="_self">I(01)</a> 
 
<b>by </b><i><a class="txt" href="borsuk_4.html#E7:67"><i><font color="Green">E63</font></i></a></i>;<br/>
<a NAME="E19:67"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="txt" href="borsuk_4.html#E1:67"><i><font color="Green">E58</font></i></a>, <a class="ref" href="jordan6.html#T56">JORDAN6:56</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span> as   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <b>by </b><i><a class="txt" href="borsuk_4.html#E19:67"><i><font color="Green">E71</font></i></a>, <a class="ref" href="pre_topc.html#T29">PRE_TOPC:29</a></i>;<br/>
<a NAME="E22:67"/><i><font color="Green">E72</font></i>: 
<span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="goboard9.html#T4">GOBOARD9:4</a></i>;<br/>
<a NAME="E23:67"/><i><font color="Green">E73</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="borsuk_4.html#E13:67"><i><font color="Green">E67</font></i></a></i>;<br/>
<a NAME="E24:67"/>
<font color="Maroon">c<sub>5</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="borsuk_4.html#E3:67"><i><font color="Green">E59</font></i></a>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>
<a NAME="E25:67"/><b>then </b><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>9</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i><a class="ref" href="funct_1.html#T84">FUNCT_1:84</a></i>;<br/>
<a NAME="E26:67"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>9</sub></font> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="txt" href="borsuk_4.html#E14:67"><i><font color="Green">E68</font></i></a>, <a class="txt" href="borsuk_4.html#E16:67"><i><font color="Green">E69</font></i></a>, <a class="txt" href="borsuk_4.html#E22:67"><i><font color="Green">E72</font></i></a>, <a class="ref" href="topmetr.html#T9">TOPMETR:9</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>12</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="partfun1.html#K2">|</a> <font color="Maroon">c<sub>10</sub></font>;<br/>
<a NAME="E27:67"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="tops_2.html#NK3" target="_self">"</a>  is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="txt" href="borsuk_4.html#E3:67"><i><font color="Green">E59</font></i></a>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>
<a NAME="E28:67"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T29">PRE_TOPC:29</a></i>;<br/>
<a NAME="E29:67"/>
<font color="Maroon">c<sub>10</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="borsuk_4.html#E19:67"><i><font color="Green">E71</font></i></a>, <a class="ref" href="pre_topc.html#T29">PRE_TOPC:29</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>13</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="partfun1.html#K2">|</a> <font color="Maroon">c<sub>10</sub></font> as   <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<a href="topmetr.html#K5">I[01]</a>  <b>by </b><i><a class="txt" href="borsuk_4.html#E28:67"><i><font color="Green">E77</font></i></a>, <a class="ref" href="funct_2.html#T38">FUNCT_2:38</a></i>;<br/>
<a NAME="E31:67"/><i><font color="Green">E78</font></i>: 
<font color="Maroon">c<sub>13</sub></font> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="txt" href="borsuk_4.html#E22:67"><i><font color="Green">E72</font></i></a>, <a class="txt" href="borsuk_4.html#E27:67"><i><font color="Green">E76</font></i></a>, <a class="ref" href="topmetr.html#T10">TOPMETR:10</a></i>;<br/>
<a NAME="E32:67"/><i><font color="Green">E79</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="borsuk_4.html#E13:67"><i><font color="Green">E67</font></i></a></i>;<br/>
<a NAME="E33:67"/>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="borsuk_4.html#E3:67"><i><font color="Green">E59</font></i></a>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>
<a NAME="E34:67"/><b>then </b>
( <font color="Maroon">c<sub>9</sub></font> <a href="tops_2.html#NK3" target="_self">"</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K2">"</a>  &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tops_2.html#NK3" target="_self">"</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K2">"</a>  )
 
<b>by </b><i><a class="txt" href="borsuk_4.html#E4:67"><i><font color="Green">E60</font></i></a>, <a class="txt" href="borsuk_4.html#E25:67"><i><font color="Green">E74</font></i></a>, <a class="txt" href="borsuk_4.html#E32:67"><i><font color="Green">E79</font></i></a>, <a class="ref" href="tops_2.html#D4">TOPS_2:def 4</a></i>;<br/>
<a NAME="E35:67"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="tops_2.html#NK3" target="_self">"</a> 
 
<b>by </b><i><a class="txt" href="borsuk_4.html#E4:67"><i><font color="Green">E60</font></i></a>, <a class="txt" href="borsuk_4.html#E11:67"><i><font color="Green">E66</font></i></a>, <a class="ref" href="rfunct_2.html#T40">RFUNCT_2:40</a></i>;<br/>
<a NAME="E36:67"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font> <a href="tops_2.html#NK3" target="_self">"</a>  is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="txt" href="borsuk_4.html#E14:67"><i><font color="Green">E68</font></i></a>, <a class="txt" href="borsuk_4.html#E31:67"><i><font color="Green">E78</font></i></a>, <a class="ref" href="topmetr.html#T9">TOPMETR:9</a></i>;<br/>
<a NAME="E37:67"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a> 
 
<b>by </b><i><a class="txt" href="borsuk_4.html#E18:67"><i><font color="Green">E70</font></i></a>, <a class="txt" href="borsuk_4.html#E23:67"><i><font color="Green">E73</font></i></a>, <a class="txt" href="borsuk_4.html#E25:67"><i><font color="Green">E74</font></i></a>, <a class="txt" href="borsuk_4.html#E26:67"><i><font color="Green">E75</font></i></a>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>
<b>hence </b><a NAME="E38:67"/>
 <a href="borsuk_4.html#K1" target="_self">I(01)</a> ,<span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span></span>)</span> <a href="t_0topsp.html#R1">are_homeomorphic</a> 
 <b>by </b><i><a class="ref" href="t_0topsp.html#D1">T_0TOPSP:def 1</a></i>;<br/>


</div>
