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<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="E2:30_3_1"/><i><font color="Green" title="E18">A4</font></i>: 
 <a href="metric_1.html#K11" title="METRIC_1:func.11">Sphere</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="topreal6.html#T70" title="TOPREAL6:th.70">TOPREAL6:70</a></i>;<br/>
<a NAME="E3:30_3_1"/>
 <a href="metric_1.html#K11" title="METRIC_1:func.11">Sphere</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#K3" title="TOPREAL9:func.3">Sphere</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#T15" target="_self" title="TOPREAL9:th.15">Th15</a></i>;<br/>
<b>hence </b><a NAME="E4:30_3_1"/>
(  <a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">r</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> &amp;  <a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</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#E2:30_3_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="jordan2c.html#D2" title="JORDAN2C:def.2">JORDAN2C:def 2</a>, <a class="ref" href="topreal6.html#T69" title="TOPREAL6:th.69">TOPREAL6:69</a></i>;<br/>


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