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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/>

<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E1:14"/>
 <a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>1</sub></font> is <a href="tex_2.html#V3">discrete</a>
 
<b>by </b><i><a class="ref" href="tex_2.html#T35">TEX_2:35</a></i>;<br/>
<a NAME="E2:14"/><b>then </b>
 <a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>1</sub></font> is <a href="tsp_1.html#V1">T_0</a>
 
<b>by </b><i><a class="ref" href="tsp_1.html#T11">TSP_1:11</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:14"/>
 <a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E5:14"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="tsp_2.html#V1" target="_self">maximal_T_0</a>
 <b>by </b><i><a class="ref" href="tsp_2.html#T9" target="_self">Th9</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
;<br/>

<b>thus </b><a NAME="E6:14"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="tsp_2.html#V1" target="_self">maximal_T_0</a>
 <b>by </b><i><a class="txt" href="tsp_2.html#E5:14"><i><font color="Green">E13</font></i></a></i>;<br/>


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