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

<span class="kw">let </span><font color="Maroon" title="c1">GX</font> be  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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">GX</font> holds  <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="connsp_1.html#R2" title="CONNSP_1:pred.2">are_joined</a>  ) implies <font color="Maroon" title="c1">GX</font> is  <a href="connsp_1.html#V1" title="CONNSP_1:attr.1">connected</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:36"/>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">GX</font> holds  <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="connsp_1.html#R2" title="CONNSP_1:pred.2">are_joined</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">GX</font> is  <a href="connsp_1.html#V1" title="CONNSP_1:attr.1">connected</a> </span><br/>

<a NAME="E2:36"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">x</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">GX</font> st <br/>for <font color="Olive" title="b2">y</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">GX</font> holds  <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="connsp_1.html#R2" title="CONNSP_1:pred.2">are_joined</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="connsp_1.html#T31" target="_self" title="CONNSP_1:th.31">Th31</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:36"/>
<font color="Maroon" title="c1">GX</font> is  <a href="connsp_1.html#V1" title="CONNSP_1:attr.1">connected</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="connsp_1.html#T30" target="_self" title="CONNSP_1:th.30">Th30</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
