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<b>let </b><font color="Maroon">X</font> be    <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">Y</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#L1">TopStruct</a> , <font color="Maroon">Z</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">X</font>,<font color="Maroon">Y</font>;<br/><b>let </b><font color="Maroon">h</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">Y</font>,<font color="Maroon">Z</font>;<br/>







<b>assume </b><a NAME="E1:4"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">h</font> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a>  &amp; <font color="Maroon">f</font> is <a href="pre_topc.html#V5">continuous</a> )
 ;<br/>

<a NAME="E2:4"/><b>then </b>
<font color="Maroon">h</font> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>
<b>hence </b><a NAME="E3:4"/>
<font color="Maroon">h</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font> is <a href="pre_topc.html#V5">continuous</a>
 <b>by </b><i>, <a class="ref" href="tops_2.html#T58">TOPS_2:58</a></i>;<br/>


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