<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E20">Th12</font></span>: <a NAME="T19"><span class="comment"><font color="firebrick">:: FINTOPO7:19</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">T</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>  ex <font color="Olive" title="b2">ET</font> being   <a href="fintopo7.html#NM3" title="FINTOPO7:NM.3">FMT_TopSpace</a> st <br/>(  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">ET</font> &amp;  <a href="fintopo7.html#K4" title="FINTOPO7:func.4">Family_open_set</a> <font color="Olive" title="b2">ET</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Olive" title="b1">T</font> )</div></div>
