<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c5">T1</font>, <font color="Maroon" title="c6">T2</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c7">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c5">T1</font>,<font color="Maroon" title="c6">T2</font>;<br/>



<b>assume </b><a NAME="E1:17"/>
<font color="Maroon" title="c7">f</font> <a href="tops_2.html#NR1" title="TOPS_2:NR.1">is_homeomorphism</a> 
 ;<br/>

<a NAME="E2:17"/><b>then </b><i><font color="Green" title="E12">A1</font></i>: 
<font color="Maroon" title="c7">f</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>
 
<b>by </b><i><a class="ref" href="tops_2.html#D5" title="TOPS_2:def.5">TOPS_2:def 5</a></i>;<br/>
<b>let </b><font color="Maroon" title="c8">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c5">T1</font>;<br/>

<b>assume </b><a NAME="E3:17"/>
<font color="Maroon" title="c8">A</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 ;<br/>

<a NAME="E4:17"/><b>then </b>
<font color="Maroon" title="c7">f</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c8">A</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 
<b>by </b><i><a class="txt" href="jordan24.html#E2:17"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="tops_2.html#T75" title="TOPS_2:th.75">TOPS_2:75</a></i>;<br/>
<b>hence </b><a NAME="E5:17"/>
<font color="Maroon" title="c7">f</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c8">A</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 ;<br/>


</div>
