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<b>let </b><font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/>

<b>reconsider </b><font color="Maroon">f</font> =  <a href="grcat_1.html#K7">id</a> <font color="Maroon">T</font> as   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">T</font>,<a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T</font> #) ;<br/>
<b>take </b>
<font color="Maroon">f</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="t_0topsp.html#D1">T_0TOPSP:def 1</a><br/>

<b>thus </b><a NAME="E2:33"/>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a><br/>

<b>thus </b> <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font> = 
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">T</font>
<b>by </b><i><a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>
<br/>.= 
 <a href="pre_topc.html#K2">[#]</a> <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T</font> #)

;<br/>

<b>thus </b><a NAME="E4:33"/>
<font color="Maroon">f</font> is <a href="funct_1.html#V2">one-to-one</a>
 ;<br/>

<b>thus </b><a NAME="E5:33"/>
<font color="Maroon">f</font> is <a href="pre_topc.html#V5">continuous</a>
 <b>by </b><i><a class="ref" href="yellow12.html#T36">YELLOW12:36</a></i>;<br/>

<a NAME="E6:33"/>
<font color="Maroon">f</font> <a href="tops_2.html#K2">/"</a>  <a href="funct_2.html#R1">=</a> <span class="p1">(<span class="default"><a href="grcat_1.html#K7">id</a> <font color="Maroon">T</font></span>)</span> <a href="tops_2.html#K2">/"</a> 
 
;<br/>
<b>hence </b><a NAME="E7:33"/>
<font color="Maroon">f</font> <a href="tops_2.html#K2">/"</a>  is <a href="pre_topc.html#V5">continuous</a>
 <b>by </b><i><a class="ref" href="yellow12.html#T36">YELLOW12:36</a></i>;<br/>


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