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<a NAME="E1:30_1_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">r</font> is   <a href="real_1.html#NM1">Real</a>
 
<b>by </b><i><a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">e</font> = <font color="Maroon">x</font> as   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14">Euclid</a> <font color="Maroon">n</font></span>)</span> <b>by </b><i><a class="ref" href="topreal3.html#T13">TOPREAL3:13</a></i>;<br/>
<a NAME="E3:30_1_1"/><i><font color="Green">E44</font></i>: 
 <a href="metric_1.html#K9">Ball</a> <font color="Maroon">e</font>,<font color="Maroon">r</font> is <a href="tbsp_1.html#V6">bounded</a>
 
<b>by </b><i><a class="ref" href="tbsp_1.html#T19">TBSP_1:19</a></i>;<br/>
<a NAME="E4:30_1_1"/>
 <a href="metric_1.html#K9">Ball</a> <font color="Maroon">e</font>,<font color="Maroon">r</font> <a href="hidden.html#R1">=</a>  <a href="topreal9.html#K1" target="_self">Ball</a> <font color="Maroon">x</font>,<font color="Maroon">r</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:30_1_1"/>
(  <a href="topreal9.html#K1" target="_self">Ball</a> <font color="Maroon">x</font>,<font color="Maroon">r</font> is <a href="pre_topc.html#V3">open</a> &amp;  <a href="topreal9.html#K1" target="_self">Ball</a> <font color="Maroon">x</font>,<font color="Maroon">r</font> is <a href="jordan2c.html#V1">Bounded</a> )
 <b>by </b><i>, , <a class="ref" href="goboard6.html#T6">GOBOARD6:6</a>, <a class="ref" href="jordan2c.html#D2">JORDAN2C:def 2</a></i>;<br/>


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