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<b>let </b><font color="Maroon" title="c1">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>;<br/><b>let </b><font color="Maroon" title="c2">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>;<br/>



<b>assume </b><a NAME="E1:50"/><i><font color="Green" title="E29">A1</font></i>: 
<font color="Maroon" title="c1">T</font> is <a href="urysohn1.html#V1" title="URYSOHN1:attr.1">being_T1</a>
 ;<br/>

<b>assume </b><a NAME="E2:50"/>
<font color="Maroon" title="c2">A</font> is <a href="topgen_1.html#V2" title="TOPGEN_1:attr.2">dense-in-itself</a>
 ;<br/>

<a NAME="E3:50"/><b>then </b>
<font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="ref" href="topgen_1.html#D7" target="_self" title="TOPGEN_1:def.7">Def7</a></i>;<br/>
<b>then </b><i><font color="Green" title="E30">A2</font></i>:  <a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Maroon" title="c2">A</font> = 
<font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Maroon" title="c2">A</font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>
<br/>.= 
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font>
<b>by </b><i><a class="ref" href="topgen_1.html#T31" target="_self" title="TOPGEN_1:th.31">Th31</a></i>
;<br/>
 <a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font></span>)</span> = 
 <a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="topgen_1.html#T31" target="_self" title="TOPGEN_1:th.31">Th31</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <span class="p2">(<span class="default"><a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="topgen_1.html#T33" target="_self" title="TOPGEN_1:th.33">Th33</a></i>
<br/>.= 
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font>
<b>by </b><i><a class="txt" href="topgen_1.html#E1:50"><i><font color="Green" title="E29">A1</font></i></a>, <a class="txt" href="topgen_1.html#E4:50"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="topgen_1.html#T34" target="_self" title="TOPGEN_1:th.34">Th34</a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>
;<br/>
<b>hence </b><a NAME="E6:50"/>
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font> is <a href="topgen_1.html#V2" title="TOPGEN_1:attr.2">dense-in-itself</a>
 <b>by </b><i><a class="ref" href="topgen_1.html#D7" target="_self" title="TOPGEN_1:def.7">Def7</a></i>;<br/>


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