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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">M</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds   <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">M</font> <a href="waybel26.html#NK2" title="WAYBEL26:NK.2">-TOP_prod</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">M</font> <a href="pre_circ.html#K1" title="PRE_CIRC:func.1">--&gt;</a> <a href="waybel18.html#K9" title="WAYBEL18:func.9">Sierpinski_Space</a> </span>)</span></span>)</span>,<font color="Olive" title="b1">M</font> <a href="waybel26.html#NK1" title="WAYBEL26:NK.1">-POS_prod</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">M</font> <a href="pre_circ.html#K1" title="PRE_CIRC:func.1">--&gt;</a> <span class="p2">(<span class="default"><a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<a href="waybel18.html#K9" title="WAYBEL18:func.9">Sierpinski_Space</a> </span>)</span></span>)</span> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">are_isomorphic</a> </span><br/><b>let </b><font color="Maroon" title="c2">M</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">M</font> <a href="waybel26.html#NK2" title="WAYBEL26:NK.2">-TOP_prod</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">M</font> <a href="pre_circ.html#K1" title="PRE_CIRC:func.1">--&gt;</a> <a href="waybel18.html#K9" title="WAYBEL18:func.9">Sierpinski_Space</a> </span>)</span></span>)</span>,<font color="Maroon" title="c2">M</font> <a href="waybel26.html#NK1" title="WAYBEL26:NK.1">-POS_prod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">M</font> <a href="pre_circ.html#K1" title="PRE_CIRC:func.1">--&gt;</a> <span class="p2">(<span class="default"><a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<a href="waybel18.html#K9" title="WAYBEL18:func.9">Sierpinski_Space</a> </span>)</span></span>)</span> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">are_isomorphic</a> </span><br/>



<b>consider </b><font color="Maroon" title="c3">F</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">M</font> <a href="waybel26.html#NK2" title="WAYBEL26:NK.2">-TOP_prod</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">M</font> <a href="pre_circ.html#K1" title="PRE_CIRC:func.1">--&gt;</a> <a href="waybel18.html#K9" title="WAYBEL18:func.9">Sierpinski_Space</a> </span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">M</font> <a href="waybel26.html#NK1" title="WAYBEL26:NK.1">-POS_prod</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">M</font> <a href="pre_circ.html#K1" title="PRE_CIRC:func.1">--&gt;</a> <span class="p3">(<span class="default"><a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<a href="waybel18.html#K9" title="WAYBEL18:func.9">Sierpinski_Space</a> </span>)</span></span>)</span></span>)</span><b> such that </b><br/><a NAME="E2:46"/><i><font color="Green" title="E38">A1</font></i>: 
<font color="Maroon" title="c3">F</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a>
 <b>and </b><br/><a NAME="E3:46"/>
for <font color="Olive" title="b1">f</font> being <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">X</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">M</font> <a href="waybel26.html#NK2" title="WAYBEL26:NK.2">-TOP_prod</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">M</font> <a href="pre_circ.html#K1" title="PRE_CIRC:func.1">--&gt;</a> <a href="waybel18.html#K9" title="WAYBEL18:func.9">Sierpinski_Space</a> </span>)</span></span>)</span> holds  <font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_6.html#K10" title="FUNCT_6:func.10">commute</a> <font color="Olive" title="b1">f</font>
 <b>by </b><i><a class="ref" href="waybel26.html#T35" target="_self" title="WAYBEL26:th.35">Th35</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">F</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D8" title="WAYBEL_1:def.8">WAYBEL_1:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">F</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a></span><br/>

<b>thus </b><a NAME="E4:46"/>
<font color="Maroon" title="c3">F</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a>
 <b>by </b><i><a class="txt" href="#E2:46"><i><font color="Green" title="E38">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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