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<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>, <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>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">S</font>,<font color="Maroon">T</font>;<br/>



<b>assume </b><a NAME="E1:43"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">f</font> is <a href="funct_1.html#V2">one-to-one</a>
 ;<br/>

<b>assume </b><a NAME="E2:43"/>
<font color="Maroon">f</font> is <a href="funct_2.html#V2">onto</a>
 ;<br/>

<a NAME="E3:43"/><b>then </b><i><font color="Green">E38</font></i>: 
 <a href="relset_1.html#K5">rng</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#D3">FUNCT_2:def 3</a></i>;<br/>
<a NAME="E4:43"/>
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">S</font>
 
<b>by </b><i>, , <a class="ref" href="tops_2.html#T62">TOPS_2:62</a></i>;<br/>
<a NAME="E5:43"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">f</font> <a href="tops_2.html#NK3" target="_self">"</a>  is <a href="funct_2.html#V2">onto</a>
 
<b>by </b><i><a class="ref" href="funct_2.html#D3">FUNCT_2:def 3</a></i>;<br/>
<a NAME="E6:43"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">f</font> <a href="tops_2.html#NK3" target="_self">"</a>  is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i>, , <a class="ref" href="tops_2.html#T63">TOPS_2:63</a></i>;<br/>
<a NAME="E7:43"/>
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="tops_2.html#NK3" target="_self">"</a>  <a href="funct_2.html#R2">=</a> <font color="Maroon">f</font>
 
<b>by </b><i>, , <a class="ref" href="tops_2.html#T64">TOPS_2:64</a></i>;<br/>
<b>hence </b><a NAME="E8:43"/>
( <font color="Maroon">f</font> is <a href="t_0topsp.html#V1">open</a> iff <font color="Maroon">f</font> <a href="tops_2.html#NK3" target="_self">"</a>  is <a href="pre_topc.html#V5">continuous</a> )
 <b>by </b><i>, , </i>;<br/>


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