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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E4">Th7</font></span>: <a NAME="T7"><span class="comment"><font color="firebrick">:: TOPALG_3:7</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> holds <br/> ( <font color="Olive" title="b1">T</font> is  <a href="connsp_1.html#V1" title="CONNSP_1:attr.1">connected</a>  iff  for <font color="Olive" title="b2">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">T</font>,<span class="p1">(<span class="default"><a href="compts_1.html#K1" title="COMPTS_1:func.1">1TopSp</a> <span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span>  holds <br/>(  not <font color="Olive" title="b2">f</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  or  not <font color="Olive" title="b2">f</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>  ) )</div></div>
