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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="compts_1.html#V5">being_T4</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be  <a href="pre_topc.html#V4">closed</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:33"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="measure5.html#K6">{}</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="urysohn3.html#M2" target="_self">Rain</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>
<b>take </b>
 <a href="urysohn3.html#K7" target="_self">Thunder</a> <font color="Maroon">c<sub>4</sub></font>
;<br/>

<b>thus </b><a NAME="E3:33"/>
(  <a href="urysohn3.html#K7" target="_self">Thunder</a> <font color="Maroon">c<sub>4</sub></font> is <a href="pre_topc.html#V5">continuous</a> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>( 0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="urysohn3.html#K7" target="_self">Thunder</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="urysohn3.html#K8" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="urysohn3.html#K7" target="_self">Thunder</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="urysohn3.html#K8" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> implies <span class="p1">(<span class="default"><a href="urysohn3.html#K7" target="_self">Thunder</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="urysohn3.html#K8" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 ) &amp; ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> implies <span class="p1">(<span class="default"><a href="urysohn3.html#K7" target="_self">Thunder</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="urysohn3.html#K8" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> 1 ) ) ) )
 <b>by </b><i><a class="txt" href="urysohn3.html#E1:33"><i><font color="Green">E29</font></i></a>, <a class="ref" href="urysohn3.html#T21" target="_self">Th21</a></i>;<br/>


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