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<b>consider </b><font color="Maroon">c<sub>1</sub></font> being  non <a href="struct_0.html#V3">empty</a> <a href="metric_1.html#V1">strict</a> <a href="metric_1.html#NM1">MetrSpace</a>;<br/>
<b>take </b><font color="Maroon">c<sub>2</sub></font> =  <a href="pcomps_1.html#K4" target="_self">TopSpaceMetr</a> <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = the <a href="metric_1.html#U1">distance</a> of <font color="Maroon">c<sub>1</sub></font> as   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>, <a href="numbers.html#K1">REAL</a>  ;<br/>
<b>thus </b><a NAME="E3:48_1_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="pre_topc.html#V1">strict</a>
 ;<br/>

<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="pcomps_1.html#D9" target="_self">PCOMPS_1:def 9</a><br/>

<b>thus </b><a NAME="E4:48_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="pcomps_1.html#R1" target="_self">is_metric_of</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="pcomps_1.html#T39" target="_self">Th39</a></i>;<br/>

<b>hence </b><a NAME="E5:48_1_1"/>
 <a href="pcomps_1.html#K3" target="_self">Family_open_set</a> <span class="p1">(<span class="default"><a href="pcomps_1.html#K5" target="_self">SpaceMetr</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="pcomps_1.html#D8" target="_self">Def8</a></i>;<br/>


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