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<b>let </b><font color="Maroon">c<sub>9</sub></font> be    <a href="pre_topc.html#M1">SubSpace</a> of  <a href="euclid.html#K15">TOP-REAL</a> 2;<br/>

<b>assume </b><a NAME="E1:33_1_1"/><i><font color="Green">E21</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>9</sub></font> is   <a href="topreal2.html#NM1">Simple_closed_curve</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="toprealb.html#D5" target="_self">TOPREALB:def 5</a><br/>

<b>then reconsider </b><font color="Maroon">c<sub>10</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>9</sub></font> as   <a href="topreal2.html#NM1">Simple_closed_curve</a> ;<br/>
<a NAME="E3:33_1_1"/>
not <font color="Maroon">c<sub>10</sub></font> is <a href="xboole_0.html#V1">empty</a>
 
;<br/>
<b>hence </b><a NAME="E4:33_1_1"/>
not the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>9</sub></font> is <a href="xboole_0.html#V1">empty</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a><br/>

<b>thus </b><a NAME="E5:33_1_1"/>
<font color="Maroon">c<sub>9</sub></font> is <a href="borsuk_2.html#V1">arcwise_connected</a>
 <b>by </b><i><a class="txt" href="toprealb.html#E1:33_1_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="topalg_3.html#T11">TOPALG_3:11</a></i>;<br/>

<a NAME="E6:33_1_1"/>
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 
;<br/>
<a NAME="E7:33_1_1"/><b>then </b>
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>9</sub></font> is <a href="compts_1.html#V6">compact</a>
 
<b>by </b><i><a class="ref" href="compts_1.html#T11">COMPTS_1:11</a></i>;<br/>
<b>hence </b><a NAME="E8:33_1_1"/>
<font color="Maroon">c<sub>9</sub></font> is <a href="compts_1.html#V2">compact</a>
 <b>by </b><i><a class="ref" href="compts_1.html#T10">COMPTS_1:10</a></i>;<br/>


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