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<div><span class="kw">theorem </span><a NAME="T40"><span class="comment"><font color="firebrick">:: NORMSP_3:40</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b3">L</font> being   <a href="lopban_1.html#V2" title="LOPBAN_1:attr.2">Lipschitzian</a>  <a href="lopban_1.html#NM1" title="LOPBAN_1:NM.1">LinearOperator</a> of <font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</font> holds <br/> (  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="normsp_3.html#K5" title="NORMSP_3:func.5">Ker</a> <font color="Olive" title="b3">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">L</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b2">Y</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Olive" title="b3">L</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b2">Y</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is  <a href="nfcont_1.html#V2" title="NFCONT_1:attr.2">closed</a>  ) <span class="kw">by</span> <span class="lab"><a class="ref" href="normsp_3.html#T31" target="_self" onmouseover="rs('normsp_3/T31')" onmouseout="rh()">LCL1</a>, <a class="ref" href="normsp_3.html#T34" target="_self" onmouseover="rs('normsp_3/T34')" onmouseout="rh()">KLXY1</a>, <a class="ref" href="normsp_3.html#T39" target="_self" onmouseover="rs('normsp_3/T39')" onmouseout="rh()">KERCL01</a>, <a class="ref" href="lopban_7.html#T6" onmouseover="rs('lopban_7/T6')" onmouseout="rh()">LOPBAN_7:6</a></span>;<br/></div></div>
