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<div><span class="kw">theorem </span><a NAME="T22"><span class="comment"><font color="firebrick">:: TEX_3:22</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y1</font>, <font color="Olive" title="b3">Y2</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>  st <font color="Olive" title="b3">Y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">Y1</font>, the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Olive" title="b2">Y1</font> #) holds <br/>( <font color="Olive" title="b2">Y1</font> is   <a href="tex_3.html#V2" title="TEX_3:attr.2">everywhere_dense</a>   <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Olive" title="b1">X</font> iff <font color="Olive" title="b3">Y2</font> is   <a href="tex_3.html#V2" title="TEX_3:attr.2">everywhere_dense</a>   <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Olive" title="b1">X</font> )</div></div>
