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<div><span class="kw">theorem </span><a NAME="T63"><span class="comment"><font color="firebrick">:: TOPS_2:63</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">GX</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>  st (  for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">GX</font>  ex <font color="Olive" title="b4">GY</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> st <br/>( <font color="Olive" title="b4">GY</font> is  <a href="connsp_1.html#V1" title="CONNSP_1:attr.1">connected</a>  &amp;  ex <font color="Olive" title="b5">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b4">GY</font>,<font color="Olive" title="b1">GX</font> st <br/>( <font color="Olive" title="b5">f</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  &amp; <font color="Olive" title="b2">x</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="b5">f</font> &amp; <font color="Olive" title="b3">y</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="b5">f</font> ) ) ) holds <br/><font color="Olive" title="b1">GX</font> is  <a href="connsp_1.html#V1" title="CONNSP_1:attr.1">connected</a> </div></div>
