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<span class="kw">let </span><font color="Maroon" title="c1">TS</font> be   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">PS</font>, <font color="Olive" title="b2">QS</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">TS</font>  st <font color="Maroon" title="c1">TS</font> is  <a href="compts_1.html#NV4" title="COMPTS_1:NV.4">Hausdorff</a>  &amp; <font color="Olive" title="b1">PS</font> is  <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>  &amp; <font color="Olive" title="b2">QS</font> is  <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>  holds <br/><font color="Olive" title="b1">PS</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b2">QS</font> is  <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">PS</font>, <font color="Maroon" title="c3">QS</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">TS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">TS</font> is  <a href="compts_1.html#NV4" title="COMPTS_1:NV.4">Hausdorff</a>  &amp; <font color="Maroon" title="c2">PS</font> is  <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>  &amp; <font color="Maroon" title="c3">QS</font> is  <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>  implies <font color="Maroon" title="c2">PS</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">QS</font> is  <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>  )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:25"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
<font color="Maroon" title="c1">TS</font> is  <a href="compts_1.html#NV4" title="COMPTS_1:NV.4">Hausdorff</a> 
 <span class="kw">and </span><br/><a NAME="E2:25"/><span class="lab"><font color="Green" title="E12">A2</font></span>: 
<font color="Maroon" title="c2">PS</font> is  <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> 
 <span class="kw">and </span><br/><a NAME="E3:25"/><span class="lab"><font color="Green" title="E13">A3</font></span>: 
<font color="Maroon" title="c3">QS</font> is  <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">PS</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">QS</font> is  <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> </span><br/>

<a NAME="E4:25"/><span class="lab"><font color="Green" title="E14">A4</font></span>: 
<font color="Maroon" title="c3">QS</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:25"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="txt" href="#E3:25"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="ref" href="compts_1.html#T16" target="_self" title="COMPTS_1:th.16">Th16</a></span>;<br/>
<a NAME="E5:25"/>
<font color="Maroon" title="c2">PS</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:25"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="txt" href="#E2:25"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="ref" href="compts_1.html#T16" target="_self" title="COMPTS_1:th.16">Th16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:25"/>
<font color="Maroon" title="c2">PS</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">QS</font> is  <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:25"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="txt" href="#E4:25"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="ref" href="compts_1.html#T18" target="_self" title="COMPTS_1:th.18">Th18</a>, <a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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