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<b>let </b><font color="Maroon" title="c1">Y</font> be    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">Y</font> is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a> implies <font color="Maroon" title="c1">Y</font> is <a href="pre_topc.html#V2" title="PRE_TOPC:attr.2">TopSpace-like</a> )</span><br/>

<b>assume </b><a NAME="E1:16_1_1"/>
<font color="Maroon" title="c1">Y</font> is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">Y</font> is <a href="pre_topc.html#V2" title="PRE_TOPC:attr.2">TopSpace-like</a></span><br/>

<a NAME="E2:16_1_1"/><b>then </b>
the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pcomps_1.html#K1" title="PCOMPS_1:func.1">bool</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">Y</font>
 
<b>by </b><i><a class="ref" href="tdlat_3.html#D1" target="_self" title="TDLAT_3:def.1">Def1</a></i>;<br/>
<a NAME="E3:16_1_1"/><b>then </b>
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">Y</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 <font color="Maroon" title="c1">Y</font> &amp; ( for <font color="Olive" title="b1">F</font> being  <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">Y</font>  st <font color="Olive" title="b1">F</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 <font color="Maroon" title="c1">Y</font> holds <br/> <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Olive" title="b1">F</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 <font color="Maroon" title="c1">Y</font> ) &amp; ( for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">Y</font>  st <font color="Olive" title="b1">A</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 <font color="Maroon" title="c1">Y</font> &amp; <font color="Olive" title="b2">B</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 <font color="Maroon" title="c1">Y</font> holds <br/><font color="Olive" title="b1">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b2">B</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 <font color="Maroon" title="c1">Y</font> ) )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#D1" title="ZFMISC_1:def.1">ZFMISC_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:16_1_1"/>
<font color="Maroon" title="c1">Y</font> is <a href="pre_topc.html#V2" title="PRE_TOPC:attr.2">TopSpace-like</a>
 <b>by </b><i><a class="ref" href="pre_topc.html#D1" title="PRE_TOPC:def.1">PRE_TOPC:def 1</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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