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<span class="kw">let </span><font color="Maroon" title="c10">S</font>, <font color="Maroon" title="c11">T</font> be    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  ex <font color="Olive" title="b1">f</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c10">S</font>,<font color="Maroon" title="c11">T</font> st <font color="Olive" title="b1">f</font> is  <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>  implies ( <font color="Maroon" title="c10">S</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  iff <font color="Maroon" title="c11">T</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  ) )</span><br/>

<span class="kw">given </span><font color="Maroon" title="c12">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c10">S</font>,<font color="Maroon" title="c11">T</font><span class="kw"> such that </span><a NAME="E2:19"/><span class="lab"><font color="Green" title="E44">A1</font></span>: 
<font color="Maroon" title="c12">f</font> is  <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c10">S</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  iff <font color="Maroon" title="c11">T</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  )</span><br/>

<a NAME="E3:19"/><span class="lab"><font color="Green" title="E45">A2</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c12">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c10">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19"><span class="lab"><font color="Green" title="E44">A1</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="E4:19"/>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c12">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c11">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="ref" href="tops_2.html#D5" title="TOPS_2:def.5">TOPS_2:def 5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:19"/>
( <font color="Maroon" title="c10">S</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  iff <font color="Maroon" title="c11">T</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="#E3:19"><span class="lab"><font color="Green" title="E45">A2</font></span></a>, <a class="txt" href="topreal2.html#E42"><span class="lab"><font color="Green" title="E41">Lm35</font></span></a>, <a class="txt" href="topreal2.html#E43"><span class="lab"><font color="Green" title="E42">Lm36</font></span></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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