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<b>let </b><font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>, <font color="Maroon">b</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">f</font> be    <a href="borsuk_2.html#M1">Path</a> of <font color="Maroon">a</font>,<font color="Maroon">b</font>;<br/>





<b>assume </b><a NAME="E1:50"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="borsuk_6.html#R1">are_connected</a> 
 ;<br/>

<a NAME="E2:50"/><i><font color="Green">E70</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</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/>
<b>reconsider </b><font color="Maroon">A</font> = <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span> as   <a href="struct_0.html#NM2">Subset</a> of <a href="topmetr.html#K3">R^1</a>  <b>by </b><i><a class="ref" href="topmetr.html#T24">TOPMETR:24</a></i>;<br/>
<b>reconsider </b><font color="Maroon">B</font> = <font color="Maroon">A</font> 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#T83">BORSUK_1:83</a></i>;<br/>
<a NAME="E5:50"/>
<font color="Maroon">A</font> is <a href="connsp_1.html#V2">connected</a>
 
<b>by </b><i><a class="ref" href="rcomp_3.html#T52">RCOMP_3:52</a></i>;<br/>
<a NAME="E6:50"/><b>then </b><i><font color="Green">E74</font></i>: 
<font color="Maroon">B</font> is <a href="connsp_1.html#V2">connected</a>
 
<b>by </b><i><a class="ref" href="connsp_1.html#T24">CONNSP_1:24</a></i>;<br/>
<a NAME="E7:50"/><i><font color="Green">E78</font></i>: 
<font color="Maroon">f</font> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i>, <a class="ref" href="borsuk_2.html#D2">BORSUK_2:def 2</a></i>;<br/>
<a NAME="E8:50"/>
<font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font>
 
<b>by </b><i>, <a class="ref" href="borsuk_1.html#T83">BORSUK_1:83</a>, <a class="ref" href="relat_1.html#T146">RELAT_1:146</a></i>;<br/>
<b>hence </b><a NAME="E9:50"/>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i>, , <a class="ref" href="tops_2.html#T75">TOPS_2:75</a></i>;<br/>


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