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<b>consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="waybel26.html#K1">oContMaps</a> <font color="Maroon">c<sub>1</sub></font>,<a href="waybel18.html#K9">Sierpinski_Space</a> </span>)</span><b> such that </b><br/><a NAME="E2:33_1_1"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="waybel_0.html#V23">isomorphic</a>
 <b>and </b><br/><a NAME="E3:33_1_1"/><i><font color="Green">E21</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> holds <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="funct_3.html#K5">chi</a> <font color="Olive">b<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="waybel26.html#T5">WAYBEL26:5</a></i>;<br/>
<a NAME="E4:33_1_1"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is <a href="funct_1.html#V2">one-to-one</a> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><a href="waybel26.html#K1">oContMaps</a> <font color="Maroon">c<sub>1</sub></font>,<a href="waybel18.html#K9">Sierpinski_Space</a> </span>)</span> )
 
<b>by </b><i><a class="txt" href="waybel29.html#E2:33_1_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/>
<a NAME="E5:33_1_1"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="tops_2.html#NK3" target="_self">"</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K2">"</a> 
 
<b>by </b><i><a class="ref" href="tops_2.html#D4">TOPS_2:def 4</a></i>;<br/>
<a NAME="E6:33_1_1"/><i><font color="Green">E24</font></i>: 
( the <a href="pre_topc.html#U1">topology</a> of <a href="waybel18.html#K9">Sierpinski_Space</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> ,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p2"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span></span><a href="enumset1.html#K1">}</a></span> &amp; the <a href="struct_0.html#U1">carrier</a> of <a href="waybel18.html#K9">Sierpinski_Space</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span> )
 
<b>by </b><i><a class="ref" href="waybel18.html#D9">WAYBEL18:def 9</a></i>;<br/>
<a NAME="E7:33_1_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <a href="waybel18.html#K9">Sierpinski_Space</a> 
 
<b>by </b><i><a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span> as  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <a href="waybel18.html#K9">Sierpinski_Space</a>  <b>by </b><i><a class="ref" href="pre_topc.html#D5">PRE_TOPC:def 5</a></i>;<br/>
<a NAME="E9:33_1_1"/><i><font color="Green">E25</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T1">YELLOW_1:1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="waybel26.html#K1">oContMaps</a> <font color="Maroon">c<sub>1</sub></font>,<a href="waybel18.html#K9">Sierpinski_Space</a> </span>)</span>;<br/><b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<a href="waybel18.html#K9">Sierpinski_Space</a>  <b>by </b><i><a class="ref" href="waybel26.html#T2">WAYBEL26:2</a></i>;<br/><a NAME="E2:33_1_1_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>3</sub></font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i><a class="ref" href="tops_2.html#T55">TOPS_2:55</a></i>;<br/><a NAME="E3:33_1_1_1"/><b>then </b><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="pre_topc.html#D5">PRE_TOPC:def 5</a></i>;<br/><i><font color="Green">E28</font></i>: <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
 <a href="funct_3.html#K5">chi</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="waybel29.html#E3:33_1_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="waybel29.html#E2:33_1_1_1"><i><font color="Green">E26</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="waybel29.html#E6:33_1_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="funct_3.html#T49">FUNCT_3:49</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><a href="waybel29.html#K4" target="_self">alpha</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> = 
<font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="waybel29.html#D4" target="_self">Def4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="waybel29.html#E4:33_1_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="waybel29.html#E5:33_1_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="waybel29.html#E9:33_1_1"><i><font color="Green">E25</font></i></a>, <a class="txt" href="waybel29.html#E3:33_1_1_1"><i><font color="Green">E27</font></i></a>, <a class="txt" href="waybel29.html#E4:33_1_1_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="funct_2.html#T32">FUNCT_2:32</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E11:33_1_1"/><b>then </b>
 <a href="waybel29.html#K4" target="_self">alpha</a> <font color="Maroon">c<sub>1</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="tops_2.html#NK3" target="_self">"</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>
<b>hence </b><a NAME="E12:33_1_1"/>
 <a href="waybel29.html#K4" target="_self">alpha</a> <font color="Maroon">c<sub>1</sub></font> is <a href="waybel_0.html#V23">isomorphic</a>
 <b>by </b><i><a class="txt" href="waybel29.html#E2:33_1_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="waybel29.html#E5:33_1_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="waybel_0.html#T68">WAYBEL_0:68</a></i>;<br/>


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