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<span class="kw">let </span><font color="Maroon" title="c1">Y</font>, <font color="Maroon" title="c2">X</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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">W</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">Y</font><br/> for <font color="Olive" title="b2">A</font> being  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">Y</font><br/> for <font color="Olive" title="b3">G</font> being   <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Olive" title="b1">W</font> holds  <font color="Olive" title="b2">A</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <font color="Olive" title="b3">G</font> is    <a href="connsp_2.html#M2" title="CONNSP_2:mode.2">a_neighborhood</a> of <font color="Olive" title="b2">A</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">W</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">W</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">Y</font><br/> for <font color="Olive" title="b2">G</font> being   <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c3">W</font> holds  <font color="Olive" title="b1">A</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <font color="Olive" title="b2">G</font> is    <a href="connsp_2.html#M2" title="CONNSP_2:mode.2">a_neighborhood</a> of <font color="Olive" title="b1">A</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">W</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">A</font> be   <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">G</font> being   <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c3">W</font> holds  <font color="Maroon" title="c4">A</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <font color="Olive" title="b1">G</font> is    <a href="connsp_2.html#M2" title="CONNSP_2:mode.2">a_neighborhood</a> of <font color="Maroon" title="c4">A</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">W</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">G</font> be    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c3">W</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">A</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <font color="Maroon" title="c5">G</font> is    <a href="connsp_2.html#M2" title="CONNSP_2:mode.2">a_neighborhood</a> of <font color="Maroon" title="c4">A</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">W</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span><br/>









<a NAME="E1:41"/>
<font color="Maroon" title="c3">W</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c5">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="connsp_2.html#D1" title="CONNSP_2:def.1">CONNSP_2:def 1</a></span>;<br/>
<a NAME="E2:41"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">W</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c5">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T37" title="ZFMISC_1:th.37">ZFMISC_1:37</a></span>;<br/>
<a NAME="E3:41"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A1</font></span>: 
<font color="Maroon" title="c4">A</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">W</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">A</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c5">G</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T178" title="RELAT_1:th.178">RELAT_1:178</a></span>;<br/>
<a NAME="E4:41"/>
<font color="Maroon" title="c4">A</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c5">G</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <font color="Maroon" title="c5">G</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T37" target="_self" title="BORSUK_1:th.37">Th37</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:41"/>
<font color="Maroon" title="c4">A</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">W</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <font color="Maroon" title="c5">G</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:41"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="connsp_2.html#D2" title="CONNSP_2:def.2">CONNSP_2:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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