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<span class="kw">let </span><font color="Maroon" title="c1">T1</font>, <font color="Maroon" title="c2">T2</font>, <font color="Maroon" title="c3">T3</font> be   <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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T1</font><br/>  for <font color="Olive" title="b2">A2</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">T2</font><br/>  for <font color="Olive" title="b3">A3</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c3">T3</font>  st <font color="Olive" title="b1">A1</font>,<font color="Olive" title="b2">A2</font> <a href="metrizts.html#R1" title="METRIZTS:pred.1">are_homeomorphic</a>  &amp; <font color="Olive" title="b2">A2</font>,<font color="Olive" title="b3">A3</font> <a href="metrizts.html#R1" title="METRIZTS:pred.1">are_homeomorphic</a>  holds <br/><font color="Olive" title="b1">A1</font>,<font color="Olive" title="b3">A3</font> <a href="metrizts.html#R1" title="METRIZTS:pred.1">are_homeomorphic</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">A1</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A2</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">T2</font><br/>  for <font color="Olive" title="b2">A3</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c3">T3</font>  st <font color="Maroon" title="c4">A1</font>,<font color="Olive" title="b1">A2</font> <a href="metrizts.html#R1" title="METRIZTS:pred.1">are_homeomorphic</a>  &amp; <font color="Olive" title="b1">A2</font>,<font color="Olive" title="b2">A3</font> <a href="metrizts.html#R1" title="METRIZTS:pred.1">are_homeomorphic</a>  holds <br/><font color="Maroon" title="c4">A1</font>,<font color="Olive" title="b2">A3</font> <a href="metrizts.html#R1" title="METRIZTS:pred.1">are_homeomorphic</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c5">A2</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">T2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A3</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c3">T3</font>  st <font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c5">A2</font> <a href="metrizts.html#R1" title="METRIZTS:pred.1">are_homeomorphic</a>  &amp; <font color="Maroon" title="c5">A2</font>,<font color="Olive" title="b1">A3</font> <a href="metrizts.html#R1" title="METRIZTS:pred.1">are_homeomorphic</a>  holds <br/><font color="Maroon" title="c4">A1</font>,<font color="Olive" title="b1">A3</font> <a href="metrizts.html#R1" title="METRIZTS:pred.1">are_homeomorphic</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c6">A3</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c3">T3</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c5">A2</font> <a href="metrizts.html#R1" title="METRIZTS:pred.1">are_homeomorphic</a>  &amp; <font color="Maroon" title="c5">A2</font>,<font color="Maroon" title="c6">A3</font> <a href="metrizts.html#R1" title="METRIZTS:pred.1">are_homeomorphic</a>  implies <font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A3</font> <a href="metrizts.html#R1" title="METRIZTS:pred.1">are_homeomorphic</a>  )</span><br/>











<span class="kw">assume </span><a NAME="E1:10"/><span class="lab"><font color="Green" title="E8">A1</font></span>: 
<font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c5">A2</font> <a href="metrizts.html#R1" title="METRIZTS:pred.1">are_homeomorphic</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c5">A2</font>,<font color="Maroon" title="c6">A3</font> <a href="metrizts.html#R1" title="METRIZTS:pred.1">are_homeomorphic</a>  or <font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A3</font> <a href="metrizts.html#R1" title="METRIZTS:pred.1">are_homeomorphic</a>  )</span><br/>

<a NAME="E2:10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E9">A2</font></span>: 
<font color="Maroon" title="c1">T1</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c2">T2</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c5">A2</font> <a href="mfold_2.html#R1" title="MFOLD_2:pred.1">are_homeomorphic</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="metrizts.html#D1" title="METRIZTS:def.1">METRIZTS:def 1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:10"/><span class="lab"><font color="Green" title="E10">A3</font></span>: 
<font color="Maroon" title="c5">A2</font>,<font color="Maroon" title="c6">A3</font> <a href="metrizts.html#R1" title="METRIZTS:pred.1">are_homeomorphic</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A3</font> <a href="metrizts.html#R1" title="METRIZTS:pred.1">are_homeomorphic</a> </span><br/>

<a NAME="E4:10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E11">A4</font></span>: 
<font color="Maroon" title="c2">T2</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c5">A2</font>,<font color="Maroon" title="c3">T3</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c6">A3</font> <a href="mfold_2.html#R1" title="MFOLD_2:pred.1">are_homeomorphic</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="metrizts.html#D1" title="METRIZTS:def.1">METRIZTS:def 1</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:10_1"/>
(  not <font color="Maroon" title="c5">A2</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  or <font color="Maroon" title="c5">A2</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_1"><span class="kw">suppose </span></a><a NAME="E1:10_1_1"/><span class="lab"><font color="Green" title="E12">A5</font></span>: 
 not <font color="Maroon" title="c5">A2</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A3</font> <a href="metrizts.html#R1" title="METRIZTS:pred.1">are_homeomorphic</a> </span><br/><div class="add"><a NAME="E2:10_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">A6</font></span>: 
(  not <font color="Maroon" title="c4">A1</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp;  not <font color="Maroon" title="c6">A3</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E3:10"><span class="lab"><font color="Green" title="E10">A3</font></span></a>, <a class="ref" href="mfold_2.html#T7" target="_self" title="MFOLD_2:th.7">Th7</a></span>;<br/><a NAME="E3:10_1_1"/>
(  not <font color="Maroon" title="c1">T1</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp;  not <font color="Maroon" title="c2">T2</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp;  not <font color="Maroon" title="c3">T3</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10_1_1"><span class="lab"><font color="Green" title="E12">A5</font></span></a>, <a class="txt" href="#E1:10"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E3:10"><span class="lab"><font color="Green" title="E10">A3</font></span></a>, <a class="ref" href="mfold_2.html#T7" target="_self" title="MFOLD_2:th.7">Th7</a></span>;<br/><a NAME="E4:10_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">T1</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c3">T3</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c6">A3</font> <a href="mfold_2.html#R1" title="MFOLD_2:pred.1">are_homeomorphic</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="txt" href="#E4:10"><span class="lab"><font color="Green" title="E11">A4</font></span></a>, <a class="txt" href="#E2:10_1_1"><span class="lab"><font color="Green" title="E13">A6</font></span></a>, <a class="txt" href="#E1:10_1_1"><span class="lab"><font color="Green" title="E12">A5</font></span></a>, <a class="ref" href="borsuk_3.html#T3" title="BORSUK_3:th.3">BORSUK_3:3</a></span>;<br/><span class="kw">hence </span><a NAME="E5:10_1_1"/>
<font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A3</font> <a href="metrizts.html#R1" title="METRIZTS:pred.1">are_homeomorphic</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="metrizts.html#D1" title="METRIZTS:def.1">METRIZTS:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_2"><span class="kw">suppose </span></a><a NAME="E1:10_1_2"/>
<font color="Maroon" title="c5">A2</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A3</font> <a href="metrizts.html#R1" title="METRIZTS:pred.1">are_homeomorphic</a> </span><br/><div class="add"><a NAME="E2:10_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E12">A7</font></span>: 
( <font color="Maroon" title="c4">A1</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; <font color="Maroon" title="c6">A3</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E3:10"><span class="lab"><font color="Green" title="E10">A3</font></span></a>, <a class="ref" href="mfold_2.html#T7" target="_self" title="MFOLD_2:th.7">Th7</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c7">f</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> ;<br/><a NAME="E4:10_1_2"/><span class="lab"><font color="Green" title="E13">A8</font></span>: 
(  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">T1</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">A1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">T3</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c6">A3</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10_1_2"><span class="lab"><font color="Green" title="E12">A7</font></span></a></span>;<br/><a NAME="E5:10_1_2"/>
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 ;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">f</font> = <font color="Maroon" title="c7">f</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">T1</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">A1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">T3</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c6">A3</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:10_1_2"><span class="lab"><font color="Green" title="E13">A8</font></span></a>, <a class="ref" href="funct_2.html#T1" title="FUNCT_2:th.1">FUNCT_2:1</a></span>;<br/><a NAME="E7:10_1_2"/><span class="lab"><font color="Green" title="E14">A9</font></span>: 
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T1</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">A1</font></span>)</span> &amp;  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">T3</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c6">A3</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:10_1_2"><span class="lab"><font color="Green" title="E13">A8</font></span></a></span>;<br/><a NAME="E8:10_1_2"/>
 for <font color="Olive" title="b1">P1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">T3</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c6">A3</font></span>)</span>  st <font color="Olive" title="b1">P1</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  holds <br/><font color="Maroon" title="c8">f</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <font color="Olive" title="b1">P1</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">P1</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">T3</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c6">A3</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c9">P1</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  implies <font color="Maroon" title="c8">f</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <font color="Maroon" title="c9">P1</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:10_1_2_1"/>
<font color="Maroon" title="c9">P1</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c8">f</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <font color="Maroon" title="c9">P1</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> </span><br/>

<a NAME="E2:10_1_2_1"/>
<font color="Maroon" title="c8">f</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <font color="Maroon" title="c9">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T137" title="RELAT_1:th.137">RELAT_1:137</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:10_1_2_1"/>
<font color="Maroon" title="c8">f</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <font color="Maroon" title="c9">P1</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E9:10_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E15">A10</font></span>: 
<font color="Maroon" title="c8">f</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_topc.html#D6" title="PRE_TOPC:def.6">PRE_TOPC:def 6</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c9">g</font> = <font color="Maroon" title="c8">f</font> as   <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>   <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#T1" title="FUNCTOR0:th.1">FUNCTOR0:1</a></span>;<br/><a NAME="E11:10_1_2"/>
 for <font color="Olive" title="b1">P1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">T1</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">A1</font></span>)</span>  st <font color="Olive" title="b1">P1</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c8">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <font color="Olive" title="b1">P1</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10_1_2"><span class="lab"><font color="Green" title="E12">A7</font></span></a></span>;<br/><a NAME="E12:10_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c8">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_topc.html#D6" title="PRE_TOPC:def.6">PRE_TOPC:def 6</a></span>;<br/><a NAME="E13:10_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c8">f</font> is  <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:10_1_2"><span class="lab"><font color="Green" title="E14">A9</font></span></a>, <a class="txt" href="#E9:10_1_2"><span class="lab"><font color="Green" title="E15">A10</font></span></a>, <a class="ref" href="tops_2.html#D5" title="TOPS_2:def.5">TOPS_2:def 5</a></span>;<br/><a NAME="E14:10_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">T1</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c3">T3</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c6">A3</font> <a href="mfold_2.html#R1" title="MFOLD_2:pred.1">are_homeomorphic</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="t_0topsp.html#D1" title="T_0TOPSP:def.1">T_0TOPSP:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E15:10_1_2"/>
<font color="Maroon" title="c4">A1</font>,<font color="Maroon" title="c6">A3</font> <a href="metrizts.html#R1" title="METRIZTS:pred.1">are_homeomorphic</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="metrizts.html#D1" title="METRIZTS:def.1">METRIZTS:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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