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

<b>let </b><font color="Maroon" title="c1">ra</font>, <font color="Maroon" title="c2">rb</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">ra</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">rb</font> implies  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> <font color="Maroon" title="c1">ra</font>,<font color="Maroon" title="c2">rb</font></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> )</span><br/>



<b>assume </b><a NAME="E1:2"/>
<font color="Maroon" title="c1">ra</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">rb</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> <font color="Maroon" title="c1">ra</font>,<font color="Maroon" title="c2">rb</font></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a></span><br/>

<a NAME="E2:2"/><b>then </b>
 <a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> <font color="Maroon" title="c1">ra</font>,<font color="Maroon" title="c2">rb</font> is <a href="connsp_1.html#V1" title="CONNSP_1:attr.1">connected</a>
 
<b>by </b><i><a class="ref" href="treal_1.html#T23" title="TREAL_1:th.23">TREAL_1:23</a></i>;<br/>
<b>hence </b><a NAME="E3:2"/>
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> <font color="Maroon" title="c1">ra</font>,<font color="Maroon" title="c2">rb</font></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="connsp_1.html#T28" title="CONNSP_1:th.28">CONNSP_1:28</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>
