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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E19">Th27</font></span>: <a NAME="T27"><span class="comment"><font color="firebrick">:: C0SP3:27</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="c0sp3.html#NM1" title="C0SP3:NM.1">NormedLinearTopSpace</a><br/>  for <font color="Olive" title="b2">RNS</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b3">s</font> being   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b4">t</font> being   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Olive" title="b2">RNS</font>  st <font color="Olive" title="b2">RNS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="normsp_1.html#G1" title="NORMSP_1:aggr.1">NORMSTR</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">X</font>, the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Olive" title="b1">X</font>, the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Olive" title="b1">X</font>, the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Olive" title="b1">X</font>, the <a href="normsp_0.html#U1" title="NORMSP_0:sel.1">normF</a> of <font color="Olive" title="b1">X</font> #) &amp; <font color="Olive" title="b3">s</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b4">t</font> holds <br/>( <font color="Olive" title="b3">s</font> is  <a href="frechet.html#V2" title="FRECHET:attr.2">convergent</a>  iff <font color="Olive" title="b4">t</font> is  <a href="normsp_1.html#V3" title="NORMSP_1:attr.3">convergent</a>  )</div></div>
