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<div><span class="kw">theorem </span><a NAME="T41"><span class="comment"><font color="firebrick">:: CLOPBAN3:41</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="clopban2.html#NM3" title="CLOPBAN2:NM.3">Complex_Banach_Algebra</a><br/>  for <font color="Olive" title="b2">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">X</font>  st <span class="p1"><a href="normsp_0.html#K2" title="NORMSP_0:func.2">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Olive" title="b1">X</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b2">x</font></span>)</span></span><a href="normsp_0.html#K2" title="NORMSP_0:func.2">.||</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 holds <br/>( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Olive" title="b1">X</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b2">x</font></span>)</span> <a href="clopban3.html#K2" title="CLOPBAN3:func.2">GeoSeq</a>  is  <a href="clopban3.html#V1" title="CLOPBAN3:attr.1">summable</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Olive" title="b1">X</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b2">x</font></span>)</span> <a href="clopban3.html#K2" title="CLOPBAN3:func.2">GeoSeq</a>  is  <a href="clopban3.html#V2" title="CLOPBAN3:attr.2">norm_summable</a>  ) <span class="kw">by</span> <span class="lab"><a class="ref" href="clopban3.html#T40" target="_self" onmouseover="rs('clopban3/T40')" onmouseout="rh()">Th40</a></span>;<br/></div></div>
