<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c2">S</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">M</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">S</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies <font color="Maroon" title="c2">S</font> is <a href="compl_sp.html#V2" title="COMPL_SP:attr.2">open</a> )</span><br/>

<b>assume </b><a NAME="E1:11_1_1"/><i><font color="Green" title="E9">Z</font></i>: 
<font color="Maroon" title="c2">S</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">S</font> is <a href="compl_sp.html#V2" title="COMPL_SP:attr.2">open</a></span><br/>

<a NAME="E2:11_1_1"/>
 <a href="pcomps_1.html#K4" title="PCOMPS_1:func.4">TopSpaceMetr</a> <font color="Maroon" title="c1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><a href="pcomps_1.html#K3" title="PCOMPS_1:func.3">Family_open_set</a> <font color="Maroon" title="c1">M</font></span>)</span> #)
 
;<br/>
<a NAME="E3:11_1_1"/><b>then </b>
<font color="Maroon" title="c2">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pcomps_1.html#K3" title="PCOMPS_1:func.3">Family_open_set</a> <font color="Maroon" title="c1">M</font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T5" title="PRE_TOPC:th.5">PRE_TOPC:5</a>, <a class="txt" href="#E1:11_1_1"><i><font color="Green" title="E9">Z</font></i></a></i>;<br/>
<a NAME="E4:11_1_1"/><b>then </b>
<font color="Maroon" title="c2">S</font> is <a href="compl_sp.html#V2" title="COMPL_SP:attr.2">open</a>
 
<b>by </b><i><a class="ref" href="compl_sp.html#D3" target="_self" title="COMPL_SP:def.3">Def3</a></i>;<br/>
<b>hence </b><a NAME="E5:11_1_1"/>
<font color="Maroon" title="c2">S</font> is <a href="compl_sp.html#V2" title="COMPL_SP:attr.2">open</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
