<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">K1</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>

<a NAME="E1:15"/>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">K1</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">K1</font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T29">PRE_TOPC:29</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">g2</font> = <a href="pscomp_1.html#K13">proj1</a>  <a href="partfun1.html#K2">|</a> <font color="Maroon">K1</font> as   <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">K1</font></span>)</span>,<a href="topmetr.html#K3">R^1</a>  <b>by </b><i><a class="ref" href="funct_2.html#T38">FUNCT_2:38</a>, <a class="ref" href="topmetr.html#T24">TOPMETR:24</a></i>;<br/>
<a NAME="E3:15"/>
for <font color="Olive">q</font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">K1</font></span>)</span> holds  <font color="Maroon">g2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">q</font> <a href="hidden.html#R1">=</a> <a href="pscomp_1.html#K13">proj1</a>  <a href="funct_1.html#K1">.</a> <font color="Olive">q</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:15"/>
<a href="pscomp_1.html#K13">proj1</a>  <a href="partfun1.html#K2">|</a> <font color="Maroon">K1</font> is  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">K1</font></span>)</span>,<a href="topmetr.html#K3">R^1</a> 
 <b>by </b><i><a class="ref" href="jgraph_2.html#T39">JGRAPH_2:39</a></i>;<br/>


</div>
