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<span class="kw">let </span><font color="Maroon" title="c4">S</font>, <font color="Maroon" title="c5">T</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">s</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c4">S</font><br/> for <font color="Olive" title="b2">t</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c5">T</font> holds   <a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> <span class="p1"><a href="borsuk_1.html#K3" title="BORSUK_1:func.3">[:</a><span class="default"><font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c5">T</font></span><a href="borsuk_1.html#K3" title="BORSUK_1:func.3">:]</a></span>,<span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[</a><span class="default"><font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">t</font></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">]</a></span>, <a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <span class="p1"><a href="group_7.html#K15" title="GROUP_7:func.15">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> <font color="Maroon" title="c4">S</font>,<font color="Olive" title="b1">s</font></span>)</span>,<span class="p2">(<span class="default"><a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> <font color="Maroon" title="c5">T</font>,<font color="Olive" title="b2">t</font></span>)</span></span><a href="group_7.html#K15" title="GROUP_7:func.15">*&gt;</a></span> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c6">s</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c4">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">t</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c5">T</font> holds   <a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> <span class="p1"><a href="borsuk_1.html#K3" title="BORSUK_1:func.3">[:</a><span class="default"><font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c5">T</font></span><a href="borsuk_1.html#K3" title="BORSUK_1:func.3">:]</a></span>,<span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[</a><span class="default"><font color="Maroon" title="c6">s</font>,<font color="Olive" title="b1">t</font></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">]</a></span>, <a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <span class="p1"><a href="group_7.html#K15" title="GROUP_7:func.15">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> <font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c6">s</font></span>)</span>,<span class="p2">(<span class="default"><a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> <font color="Maroon" title="c5">T</font>,<font color="Olive" title="b1">t</font></span>)</span></span><a href="group_7.html#K15" title="GROUP_7:func.15">*&gt;</a></span> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c7">t</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c5">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> <span class="p1"><a href="borsuk_1.html#K3" title="BORSUK_1:func.3">[:</a><span class="default"><font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c5">T</font></span><a href="borsuk_1.html#K3" title="BORSUK_1:func.3">:]</a></span>,<span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[</a><span class="default"><font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">]</a></span>, <a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <span class="p1"><a href="group_7.html#K15" title="GROUP_7:func.15">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> <font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c6">s</font></span>)</span>,<span class="p2">(<span class="default"><a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> <font color="Maroon" title="c5">T</font>,<font color="Maroon" title="c7">t</font></span>)</span></span><a href="group_7.html#K15" title="GROUP_7:func.15">*&gt;</a></span> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> </span><br/>







<span class="kw">take </span>
 <a href="topalg_4.html#K13" title="TOPALG_4:func.13">FGPrIso</a> <font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font>
; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="group_6.html#D15" title="GROUP_6:def.15">GROUP_6:def 15</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="topalg_4.html#K13" title="TOPALG_4:func.13">FGPrIso</a> <font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> </span><br/>

<span class="kw">thus </span><a NAME="E1:45"/>
 <a href="topalg_4.html#K13" title="TOPALG_4:func.13">FGPrIso</a> <font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="topalg_4.html#T29" target="_self" title="TOPALG_4:th.29">Th29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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