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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:116"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:116"/><b>then </b>
for <font color="Olive">b<sub>1</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>3</sub></font> holds <span class="p1">(<span class="default"><a href="tmap_1.html#K7" target="_self">modid</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tmap_1.html#K2" target="_self">|</a> <font color="Maroon">c<sub>3</sub></font> <a href="tmap_1.html#R1" target="_self">is_continuous_at</a> <font color="Olive">b<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="tmap_1.html#T110" target="_self">Th110</a></i>;<br/>
<b>hence </b><a NAME="E3:116"/>
<span class="p1">(<span class="default"><a href="tmap_1.html#K7" target="_self">modid</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tmap_1.html#K2" target="_self">|</a> <font color="Maroon">c<sub>3</sub></font> is  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="tmap_1.html#K6" target="_self">modified_with_respect_to</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="tmap_1.html#T49" target="_self">Th49</a></i>;<br/>


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