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<b>let </b><font color="Maroon" title="c3">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">f</font> is <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a> implies <font color="Maroon" title="c3">f</font> is <a href="t_0topsp.html#V1" title="T_0TOPSP:attr.1">open</a> )</span><br/>

<b>assume </b><a NAME="E1:39_1_1"/><i><font color="Green" title="E24">A1</font></i>: 
<font color="Maroon" title="c3">f</font> is <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">f</font> is <a href="t_0topsp.html#V1" title="T_0TOPSP:attr.1">open</a></span><br/>

<b>let </b><font color="Maroon" title="c4">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="t_0topsp.html#D2" title="T_0TOPSP:def.2">T_0TOPSP:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c4">A</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> or <font color="Maroon" title="c3">f</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c4">A</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> )</span><br/>

<b>thus </b><a NAME="E2:39_1_1"/>
(  not <font color="Maroon" title="c4">A</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> or <font color="Maroon" title="c3">f</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c4">A</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> )
 <b>by </b><i><a class="txt" href="#E1:39_1_1"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="topgrp_1.html#T25" target="_self" title="TOPGRP_1:th.25">Th25</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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