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<div><span class="kw">theorem </span><a NAME="T22"><span class="comment"><font color="firebrick">:: RLTOPSP1:22</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a><br/>  for <font color="Olive" title="b2">M</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">X</font> holds <br/> ( <font color="Olive" title="b2">M</font> is  <a href="convex1.html#V1" title="CONVEX1:attr.1">convex</a>  iff  for <font color="Olive" title="b3">u</font>, <font color="Olive" title="b4">w</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b3">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">M</font> &amp; <font color="Olive" title="b4">w</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">M</font> holds <br/> <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">w</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">M</font> )</div></div>
