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<b>let </b><font color="Maroon">P</font> be   <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/>

<b>assume </b><a NAME="E1:49"/>
<font color="Maroon">P</font> <a href="topreal1.html#NR3" target="_self">is_S-P_arc</a> 
 ;<br/>

<b>then consider </b><font color="Maroon">p1</font> being   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>, <font color="Maroon">p2</font> being   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span><b> such that </b><br/><a NAME="E3:49"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">P</font> <a href="topreal1.html#R1" target="_self">is_an_arc_of</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>
 <b>by </b><i/>;<br/>
<a NAME="E4:49"/>
 ex <font color="Olive">f</font> being  <a href="struct_0.html#NM6">Function</a> of <a href="topmetr.html#K5">I[01]</a> ,<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">P</font></span>)</span> st <br/>( <font color="Olive">f</font> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a>  &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:49"/>
 ex <font color="Olive">f</font> being  <a href="struct_0.html#NM6">Function</a> of <a href="topmetr.html#K5">I[01]</a> ,<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">P</font></span>)</span> st <font color="Olive">f</font> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a> 
 ;<br/>


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