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<span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">b</font> implies  <a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>) is  <a href="borsuk_2.html#V1" title="BORSUK_2:attr.1">pathwise_connected</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:25"/>
<font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">b</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>) is  <a href="borsuk_2.html#V1" title="BORSUK_2:attr.1">pathwise_connected</a> </span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">X</font> =  <a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>) as   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="topalg_2.html#V2" title="TOPALG_2:attr.2">interval</a>   <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of  <a href="topalg_2.html#K2" title="TOPALG_2:func.2">R^1</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="topalg_2.html#T9" target="_self" onmouseover="rs('topalg_2/T9')" onmouseout="rh()">Th9</a></span>;<br/>
<a NAME="E3:25"/>
<font color="Maroon" title="c4">X</font> is  <a href="borsuk_2.html#V1" title="BORSUK_2:attr.1">pathwise_connected</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E4:25"/>
 <a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>) is  <a href="borsuk_2.html#V1" title="BORSUK_2:attr.1">pathwise_connected</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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