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<span class="kw">thus </span><a NAME="E1:24_1_1"/>
 <a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">D</font> is  <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">D</font> is  <a href="pre_topc.html#V2" title="PRE_TOPC:attr.2">TopSpace-like</a> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">T</font> =  <a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">D</font>;<br/>
<a NAME="E2:24_1_1"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
 for <font color="Olive" title="b1">X</font> being   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <span class="p1">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">D</font></span>)</span>  st <font color="Olive" title="b1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">D</font></span>)</span> holds <br/> <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Olive" title="b1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">D</font></span>)</span>
 
;<br/>
<a NAME="E3:24_1_1"/><span class="lab"><font color="Green" title="E14">A2</font></span>: 
 for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">D</font></span>)</span>  st <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">D</font></span>)</span> &amp; <font color="Olive" title="b2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">D</font></span>)</span> holds <br/><font color="Olive" title="b1">p</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">D</font></span>)</span>
 
;<br/>
<a NAME="E4:24_1_1"/>
<font color="Maroon" title="c1">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <font color="Maroon" title="c1">D</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#D1" title="ZFMISC_1:def.1">ZFMISC_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:24_1_1"/>
 <a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <font color="Maroon" title="c1">D</font> is  <a href="pre_topc.html#V2" title="PRE_TOPC:attr.2">TopSpace-like</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:24_1_1"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E3:24_1_1"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="ref" href="pre_topc.html#D1" title="PRE_TOPC:def.1">PRE_TOPC:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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