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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E7">Th7</font></span>: <a NAME="T7"><span class="comment"><font color="firebrick">:: T_1TOPSP:7</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">T</font>, <font color="Olive" title="b2">T1</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><br/>  for <font color="Olive" title="b3">f</font> being   <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">T</font>,<font color="Olive" title="b2">T1</font>  st <font color="Olive" title="b2">T1</font> is  <a href="pre_topc.html#V7" title="PRE_TOPC:attr.7">T_1</a>  holds <br/> for <font color="Olive" title="b4">w</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b4">w</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="t_1topsp.html#K2" title="T_1TOPSP:func.2">T_1-reflex</a> <font color="Olive" title="b1">T</font></span>)</span> holds <br/> ex <font color="Olive" title="b5">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b2">T1</font> st <br/>( <font color="Olive" title="b5">z</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b3">f</font> &amp; <font color="Olive" title="b4">w</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">f</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b5">z</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )</div></div>
