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<b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</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> ;<br/>



<b>assume </b><a NAME="E1:32"/>
<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>
 ;<br/>

<b>then reconsider </b><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#V3" title="STRUCT_0:attr.3">empty</a> <a href="topalg_2.html#V3" title="TOPALG_2:attr.3">convex</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of  <a href="topalg_2.html#K3" title="TOPALG_2:func.3">R^1</a>  <b>by </b><i><a class="ref" href="topalg_2.html#T13" target="_self" title="TOPALG_2:th.13">Th13</a></i>;<br/>
<a NAME="E3:32"/>
<font color="Maroon" title="c4">X</font> is <a href="borsuk_2.html#V1" title="BORSUK_2:attr.1">arcwise_connected</a>
 
;<br/>
<b>hence </b><a NAME="E4:32"/>
 <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">arcwise_connected</a>
 ;<br/>


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