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<b>let </b><font color="Maroon" title="c1">f</font> be  non <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> <a href="goboard5.html#V2" title="GOBOARD5:attr.2">standard</a> <a href="goboard5.html#NM1" title="GOBOARD5:NM.1">special_circular_sequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp;  <a href="goboard9.html#K3" title="GOBOARD9:func.3">RightComp</a> <font color="Maroon" title="c1">f</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> )</span><br/>

<a NAME="E1:26"/>
 <a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 
<b>by </b><i><a class="ref" href="sppol_1.html#T49" title="SPPOL_1:th.49">SPPOL_1:49</a></i>;<br/>
<a NAME="E2:26"/><b>then </b><i><font color="Green" title="E10">A1</font></i>: 
<span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 
<b>by </b><i><a class="ref" href="tops_1.html#T29" title="TOPS_1:th.29">TOPS_1:29</a></i>;<br/>
<a NAME="E3:26"/>
 <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font> <a href="connsp_1.html#R4" title="CONNSP_1:pred.4">is_a_component_of</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 
<b>by </b><i><a class="ref" href="goboard9.html#D1" title="GOBOARD9:def.1">GOBOARD9:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:26"/>
 <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>by </b><i><a class="txt" href="sprect_3.html#E2:26"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="sprect_3.html#T18" target="_self" title="SPRECT_3:th.18">Th18</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="goboard9.html#K3" title="GOBOARD9:func.3">RightComp</a> <font color="Maroon" title="c1">f</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a></span><br/>

<a NAME="E5:26"/>
 <a href="goboard9.html#K3" title="GOBOARD9:func.3">RightComp</a> <font color="Maroon" title="c1">f</font> <a href="connsp_1.html#R4" title="CONNSP_1:pred.4">is_a_component_of</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 
<b>by </b><i><a class="ref" href="goboard9.html#D2" title="GOBOARD9:def.2">GOBOARD9:def 2</a></i>;<br/>
<b>hence </b><a NAME="E6:26"/>
 <a href="goboard9.html#K3" title="GOBOARD9:func.3">RightComp</a> <font color="Maroon" title="c1">f</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>by </b><i><a class="txt" href="sprect_3.html#E2:26"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="sprect_3.html#T18" target="_self" title="SPRECT_3:th.18">Th18</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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