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<div><span class="kw">theorem </span><a NAME="T26"><span class="comment"><font color="firebrick">:: NAGATA_1:26</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="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">T</font>,<span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> ( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">T</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">T1</font>)</span>)</span>  st (  for <font color="Olive" title="b4">p</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">T</font> holds  <font color="Olive" title="b3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">p</font> is   <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> ) holds <br/> for <font color="Olive" title="b4">S</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">T</font>,<span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">T</font></span>)</span>  st (  for <font color="Olive" title="b5">p</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">T</font> holds <br/> ( <font color="Olive" title="b5">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">p</font> &amp; <font color="Olive" title="b4">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">p</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  &amp; (  for <font color="Olive" title="b6">p</font>, <font color="Olive" title="b7">q</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">T</font>  st <font color="Olive" title="b6">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b7">q</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b6">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b7">q</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">p</font> ) ) ) holds <br/><font color="Olive" title="b3">F</font> <a href="nagata_1.html#K4" title="NAGATA_1:func.4">Toler</a>  is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> </div></div>
