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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E18">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: TEX_3:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a><br/>  for <font color="Olive" title="b2">X1</font>, <font color="Olive" title="b3">X2</font> being    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b2">X1</font>,<font color="Olive" title="b3">X2</font> <a href="tsep_2.html#R3" title="TSEP_2:pred.3">constitute_a_decomposition</a>  holds <br/>( <font color="Olive" title="b2">X1</font> is  <a href="tex_3.html#V1" title="TEX_3:attr.1">dense</a>  iff <font color="Olive" title="b3">X2</font> is  <a href="tex_3.html#V3" title="TEX_3:attr.3">boundary</a>  )</div></div>
