<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">Y</font> be   <a href="t_0topsp.html#NM1" title="T_0TOPSP:NM.1">T_0-TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">Y</font> is <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> iff for <font color="Olive" title="b1">X</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   <a href="waybel29.html#K3" title="WAYBEL29:func.3">Theta</a> <font color="Olive" title="b1">X</font>,<font color="Maroon" title="c1">Y</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a> )</span><br/>

<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( for <font color="Olive" title="b1">X</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   <a href="waybel29.html#K3" title="WAYBEL29:func.3">Theta</a> <font color="Olive" title="b1">X</font>,<font color="Maroon" title="c1">Y</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a> ) implies  <a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">Y</font> is <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> )</span>
<div class="add"><b>assume </b><a NAME="E1:52_1"/>
 <a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">Y</font> is <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">S<sub>3</sub></font>[<font color="Maroon" title="c1">Y</font>]</span><br/><a NAME="E2:52_1"/><b>then </b>
<font color="Maroon">S<sub>6</sub></font>[<font color="Maroon" title="c1">Y</font>]
 <b>by </b><i><a class="txt" href="waybel29.html#E40"><i><font color="Green" title="E27">Lm8</font></i></a></i>;<br/><a NAME="E3:52_1"/><b>then </b>
<font color="Maroon">S<sub>4</sub></font>[<font color="Maroon" title="c1">Y</font>]
 <b>by </b><i><a class="txt" href="waybel29.html#E38"><i><font color="Green" title="E25">Lm6</font></i></a></i>;<br/><b>hence </b><a NAME="E4:52_1"/>
<font color="Maroon">S<sub>3</sub></font>[<font color="Maroon" title="c1">Y</font>]
 <b>by </b><i><a class="txt" href="waybel29.html#E35"><i><font color="Green" title="E22">Lm3</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:52"/>
<font color="Maroon">S<sub>3</sub></font>[<font color="Maroon" title="c1">Y</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">Y</font> is <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a></span><br/>

<a NAME="E3:52"/><b>then </b>
<font color="Maroon">S<sub>4</sub></font>[<font color="Maroon" title="c1">Y</font>]
 
<b>by </b><i><a class="txt" href="waybel29.html#E33"><i><font color="Green" title="E20">Lm2</font></i></a></i>;<br/>
<a NAME="E4:52"/><b>then </b>
<font color="Maroon">S<sub>5</sub></font>[<font color="Maroon" title="c1">Y</font>]
 
<b>by </b><i><a class="txt" href="waybel29.html#E36"><i><font color="Green" title="E23">Lm4</font></i></a></i>;<br/>
<a NAME="E5:52"/><b>then </b>
<font color="Maroon">S<sub>6</sub></font>[<font color="Maroon" title="c1">Y</font>]
 
<b>by </b><i><a class="txt" href="waybel29.html#E37"><i><font color="Green" title="E24">Lm5</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:52"/>
 <a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">Y</font> is <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a>
 <b>by </b><i><a class="txt" href="waybel29.html#E39"><i><font color="Green" title="E26">Lm7</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
