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<div><span class="kw">theorem </span><a NAME="T9"><span class="comment"><font color="firebrick">:: BROUWER2:9</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">A</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="convex1.html#V1" title="CONVEX1:attr.1">convex</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Olive" title="b1">n</font></span>)</span>  st <font color="Olive" title="b2">A</font> is  <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>  &amp;  not <font color="Olive" title="b2">A</font> is  <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a>  holds <br/> for <font color="Olive" title="b3">FR</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Olive" title="b2">A</font>  st  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Olive" title="b3">FR</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tops_1.html#K2" title="TOPS_1:func.2">Fr</a> <font color="Olive" title="b2">A</font> holds <br/> not <font color="Olive" title="b3">FR</font> <a href="borsuk_1.html#R1" title="BORSUK_1:pred.1">is_a_retract_of</a> <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Olive" title="b2">A</font></div></div>
