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<a NAME="E1:30_1_1"/><i><font color="Green" title="E18">A1</font></i>: 
<font color="Maroon" title="c3">r</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>
 
<b>by </b><i><a class="ref" href="xreal_0.html#D1" title="XREAL_0:def.1">XREAL_0:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">e</font> = <font color="Maroon" title="c2">x</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14" title="EUCLID:func.14">Euclid</a> <font color="Maroon" title="c1">n</font></span>)</span> <b>by </b><i><a class="ref" href="topreal3.html#T13" title="TOPREAL3:th.13">TOPREAL3:13</a></i>;<br/>
<a NAME="E3:30_1_1"/><i><font color="Green" title="E19">A2</font></i>: 
 <a href="metric_1.html#K9" title="METRIC_1:func.9">Ball</a> <font color="Maroon" title="c4">e</font>,<font color="Maroon" title="c3">r</font> is <a href="tbsp_1.html#V6" title="TBSP_1:attr.6">bounded</a>
 
<b>by </b><i><a class="ref" href="tbsp_1.html#T19" title="TBSP_1:th.19">TBSP_1:19</a></i>;<br/>
<a NAME="E4:30_1_1"/>
 <a href="metric_1.html#K9" title="METRIC_1:func.9">Ball</a> <font color="Maroon" title="c4">e</font>,<font color="Maroon" title="c3">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal9.html#K1" title="TOPREAL9:func.1">Ball</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">r</font>
 
<b>by </b><i><a class="ref" href="topreal9.html#T13" target="_self" title="TOPREAL9:th.13">Th13</a></i>;<br/>
<b>hence </b><a NAME="E5:30_1_1"/>
(  <a href="topreal9.html#K1" title="TOPREAL9:func.1">Ball</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">r</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp;  <a href="topreal9.html#K1" title="TOPREAL9:func.1">Ball</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">r</font> is <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a> )
 <b>by </b><i><a class="txt" href="topreal9.html#E1:30_1_1"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="topreal9.html#E3:30_1_1"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="goboard6.html#T6" title="GOBOARD6:th.6">GOBOARD6:6</a>, <a class="ref" href="jordan2c.html#D2" title="JORDAN2C:def.2">JORDAN2C:def 2</a></i>;<br/>


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