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<b>let </b><font color="Maroon">T1</font> be   <a href="pre_topc.html#NM1">TopSpace</a>, <font color="Maroon">T2</font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/>

<b>assume </b><a NAME="E1:10"/><i><font color="Green">E37</font></i>: 
for <font color="Olive">A</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">A</font> is  <a href="pre_topc.html#V4">closed</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T1</font> iff <font color="Olive">A</font> is  <a href="pre_topc.html#V4">closed</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T2</font> )
 ;<br/>

<a NAME="E2:10"/>
the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T1</font> <a href="hidden.html#R1">=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:10_1"/>
the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T1</font> <a href="tarski.html#R1">c=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T2</font>
 <b>by </b><i>, </i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<b>thus </b><a NAME="E2:10_1"/>
the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T2</font> <a href="tarski.html#R1">c=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T1</font>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:10"/>
 <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T1</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T1</font> #) <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T2</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T2</font> #)
 <b>by </b><i>, </i>;<br/>


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