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<div><span class="kw">theorem </span><a NAME="T42"><span class="comment"><font color="firebrick">:: TOPGRP_1:42</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">T</font> being   <a href="topgrp_1.html#NM4" title="TOPGRP_1:NM.4">TopGroup</a>  st (  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">T</font><br/>  for <font color="Olive" title="b4">W</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Olive" title="b2">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">b</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a></span>)</span>  ex <font color="Olive" title="b5">A</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Olive" title="b2">a</font> ex <font color="Olive" title="b6">B</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Olive" title="b3">b</font> st <font color="Olive" title="b5">A</font> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">B</font> <a href="group_2.html#K1" title="GROUP_2:func.1">"</a></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">W</font> ) holds <br/><font color="Olive" title="b1">T</font> is   <a href="topgrp_1.html#NM5" title="TOPGRP_1:NM.5">TopologicalGroup</a></div></div>
