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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="pencil_2.html#NM2">Collineation</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<a NAME="E1:22"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="funct_2.html#V3">bijective</a>
 
<b>by </b><i><a class="ref" href="pencil_2.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E2:22"/><b>then </b><i><font color="Green">E15</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="funct_2.html#V2">onto</a> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D4">FUNCT_2:def 4</a></i>;<br/>
<a NAME="E3:22"/><b>then </b>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 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="funct_2.html#D3">FUNCT_2:def 3</a></i>;<br/>
<a NAME="E4:22"/><b>then </b><i><font color="Green">E16</font></i>: 
 <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> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T12">PRE_TOPC:12</a></i>;<br/>
<a NAME="E5:22"/>
<font color="Maroon">c<sub>2</sub></font> <a href="tops_2.html#NK3" target="_self">"</a>  is <a href="pencil_2.html#V1" target="_self">isomorphic</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:22_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="tops_2.html#NK3" target="_self">"</a>  is <a href="funct_2.html#V3">bijective</a> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="tops_2.html#NK3" target="_self">"</a>  is <a href="t_0topsp.html#V1">open</a> )
 <b>by </b><i><a class="ref" href="pencil_2.html#D4" target="_self">Def4</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="pencil_2.html#D4" target="_self">PENCIL_2:def 4</a><br/>

<a NAME="E2:22_1"/>
<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="tops_2.html#NK3" target="_self">"</a>  <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="pencil_2.html#E2:22"><i><font color="Green">E15</font></i></a>, <a class="txt" href="pencil_2.html#E4:22"><i><font color="Green">E16</font></i></a>, <a class="ref" href="tops_2.html#T64">TOPS_2:64</a></i>;<br/>
<b>hence </b><a NAME="E3:22_1"/>
( <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="tops_2.html#NK3" target="_self">"</a>  is <a href="funct_2.html#V3">bijective</a> &amp; <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="tops_2.html#NK3" target="_self">"</a>  is <a href="t_0topsp.html#V1">open</a> )
 <b>by </b><i><a class="ref" href="pencil_2.html#D4" target="_self">Def4</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:22"/>
<font color="Maroon">c<sub>2</sub></font> <a href="tops_2.html#NK3" target="_self">"</a>  is   <a href="pencil_2.html#NM2">Collineation</a> of <font color="Maroon">c<sub>1</sub></font>
 ;<br/>


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