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<b>let </b><font color="Maroon" title="c2">S</font>, <font color="Maroon" title="c3">T</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c4">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">T</font>;<br/>



<b>assume </b><a NAME="E1:29"/><i><font color="Green" title="E11">A1</font></i>: 
<font color="Maroon" title="c4">f</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 ;<br/>

<b>assume </b><a NAME="E2:29"/>
<font color="Maroon" title="c4">f</font> is <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>
 ;<br/>

<a NAME="E3:29"/><b>then </b><i><font color="Green" title="E12">A2</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c3">T</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D3" title="FUNCT_2:def.3">FUNCT_2:def 3</a></i>;<br/>
<a NAME="E4:29"/><b>then </b>
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">S</font>
 
<b>by </b><i><a class="txt" href="topreala.html#E1:29"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="tops_2.html#T62" title="TOPS_2:th.62">TOPS_2:62</a></i>;<br/>
<a NAME="E5:29"/><b>then </b><i><font color="Green" title="E13">A3</font></i>: 
<font color="Maroon" title="c4">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  is <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>
 
<b>by </b><i><a class="ref" href="funct_2.html#D3" title="FUNCT_2:def.3">FUNCT_2:def 3</a></i>;<br/>
<a NAME="E6:29"/><i><font color="Green" title="E14">A4</font></i>: 
<font color="Maroon" title="c4">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="topreala.html#E1:29"><i><font color="Green" title="E11">A1</font></i></a>, <a class="txt" href="topreala.html#E3:29"><i><font color="Green" title="E12">A2</font></i></a>, <a class="ref" href="tops_2.html#T63" title="TOPS_2:th.63">TOPS_2:63</a></i>;<br/>
<a NAME="E7:29"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">f</font>
 
<b>by </b><i><a class="txt" href="topreala.html#E1:29"><i><font color="Green" title="E11">A1</font></i></a>, <a class="txt" href="topreala.html#E3:29"><i><font color="Green" title="E12">A2</font></i></a>, <a class="ref" href="tops_2.html#T64" title="TOPS_2:th.64">TOPS_2:64</a></i>;<br/>
<b>hence </b><a NAME="E8:29"/>
( <font color="Maroon" title="c4">f</font> is <a href="t_0topsp.html#V1" title="T_0TOPSP:attr.1">open</a> iff <font color="Maroon" title="c4">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> )
 <b>by </b><i><a class="txt" href="topreala.html#E5:29"><i><font color="Green" title="E13">A3</font></i></a>, <a class="txt" href="topreala.html#E6:29"><i><font color="Green" title="E14">A4</font></i></a>, <a class="ref" href="topreala.html#T34" target="_self" title="TOPREALA:th.34">Th34</a></i>;<br/>


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