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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="topgen_5.html#K1" target="_self">y=0-line</a> ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>2</sub></font> =  <a href="topgen_5.html#K1" target="_self">y=0-line</a>  as  <a href="pre_topc.html#V4">closed</a> <a href="struct_0.html#NM2">Subset</a> of <a href="topgen_5.html#K3" target="_self">Niemytzki-plane</a>  <b>by </b><i><a class="ref" href="topgen_5.html#T30" target="_self">Th30</a></i>;<br/>
<a NAME="E2:53"/>
<font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>1</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <a href="topgen_5.html#K3" target="_self">Niemytzki-plane</a>  <b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E4:53"/>
 <a href="topgen_1.html#K2">Der</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="topgen_1.html#K2">Der</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="topgen_1.html#T32">TOPGEN_1:32</a></i>;<br/>
<a NAME="E5:53"/><b>then </b>
 <a href="topgen_1.html#K2">Der</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="topgen_5.html#T45" target="_self">Th45</a></i>;<br/>
<a NAME="E6:53"/><b>then </b>
 <a href="topgen_1.html#K2">Der</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/>
<a NAME="E7:53"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K2">\/</a> <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="topgen_1.html#T31">TOPGEN_1:31</a></i>;<br/>
<b>hence </b><a NAME="E8:53"/>
<font color="Maroon">c<sub>1</sub></font> is  <a href="pre_topc.html#V4">closed</a> <a href="struct_0.html#NM2">Subset</a> of <a href="topgen_5.html#K3" target="_self">Niemytzki-plane</a> 
 ;<br/>


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