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<span class="kw">set </span><font color="Maroon" title="c3">T</font> =  <a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c2">A</font>;<br/>
<a NAME="E1:66_1_1"/><span class="lab"><font color="Green" title="E37">A1</font></span>: 
(  <a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c2">A</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  &amp;  <a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a></span>)</span> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrtop1.html#T47" target="_self" title="MATRTOP1:th.47">Th47</a></span>;<br/>
<a NAME="E2:66_1_1"/><span class="lab"><font color="Green" title="E38">A2</font></span>: 
 <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="laplace.html#T34" title="LAPLACE:th.34">LAPLACE:34</a></span>;<br/>
<a NAME="E3:66_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A3</font></span>: 
<span class="p1">(<span class="default"><a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrtop1.html#T43" target="_self" title="MATRTOP1:th.43">Th43</a></span>;<br/>
<a NAME="E4:66_1_1"/><span class="lab"><font color="Green" title="E40">A4</font></span>: 
(  <a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c2">A</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>  &amp;  <a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c2">A</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:66_1_1"><span class="lab"><font color="Green" title="E38">A2</font></span></a>, <a class="ref" href="matrtop1.html#T40" target="_self" title="MATRTOP1:th.40">Th40</a>, <a class="ref" href="matrtop1.html#T42" target="_self" title="MATRTOP1:th.42">Th42</a></span>;<br/>
<a NAME="E5:66_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A5</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D3" title="FUNCT_2:def.3">FUNCT_2:def 3</a></span>;<br/>
<a NAME="E6:66_1_1"/>
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="tops_2.html#K2" title="TOPS_2:func.2">/"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:66_1_1"><span class="lab"><font color="Green" title="E40">A4</font></span></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="tops_2.html#D4" title="TOPS_2:def.4">TOPS_2:def 4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:66_1_1"/>
 <a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c2">A</font> is  <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:66_1_1"><span class="lab"><font color="Green" title="E40">A4</font></span></a>, <a class="txt" href="#E3:66_1_1"><span class="lab"><font color="Green" title="E39">A3</font></span></a>, <a class="txt" href="#E1:66_1_1"><span class="lab"><font color="Green" title="E37">A1</font></span></a>, <a class="txt" href="#E5:66_1_1"><span class="lab"><font color="Green" title="E41">A5</font></span></a>, <a class="ref" href="tops_2.html#D5" title="TOPS_2:def.5">TOPS_2:def 5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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