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<b>let </b><font color="Maroon" title="c1">T</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="borsuk_2.html#V1" title="BORSUK_2:attr.1">arcwise_connected</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">y0</font>, <font color="Olive" title="b2">y1</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font><br/> for <font color="Olive" title="b3">R</font>, <font color="Olive" title="b4">V</font> being   <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Olive" title="b1">y0</font>,<font color="Olive" title="b2">y1</font>  st <font color="Olive" title="b3">R</font>,<font color="Olive" title="b4">V</font> <a href="borsuk_2.html#R4" title="BORSUK_2:pred.4">are_homotopic</a>  holds <br/> <a href="topalg_1.html#K4" title="TOPALG_1:func.4">pi_1-iso</a> <font color="Olive" title="b3">R</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="topalg_1.html#K4" title="TOPALG_1:func.4">pi_1-iso</a> <font color="Olive" title="b4">V</font></span><br/><b>let </b><font color="Maroon" title="c2">y0</font>, <font color="Maroon" title="c3">y1</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">R</font>, <font color="Olive" title="b2">V</font> being   <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c2">y0</font>,<font color="Maroon" title="c3">y1</font>  st <font color="Olive" title="b1">R</font>,<font color="Olive" title="b2">V</font> <a href="borsuk_2.html#R4" title="BORSUK_2:pred.4">are_homotopic</a>  holds <br/> <a href="topalg_1.html#K4" title="TOPALG_1:func.4">pi_1-iso</a> <font color="Olive" title="b1">R</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="topalg_1.html#K4" title="TOPALG_1:func.4">pi_1-iso</a> <font color="Olive" title="b2">V</font></span><br/><b>let </b><font color="Maroon" title="c4">R</font>, <font color="Maroon" title="c5">V</font> be    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c2">y0</font>,<font color="Maroon" title="c3">y1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">R</font>,<font color="Maroon" title="c5">V</font> <a href="borsuk_2.html#R4" title="BORSUK_2:pred.4">are_homotopic</a>  implies  <a href="topalg_1.html#K4" title="TOPALG_1:func.4">pi_1-iso</a> <font color="Maroon" title="c4">R</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="topalg_1.html#K4" title="TOPALG_1:func.4">pi_1-iso</a> <font color="Maroon" title="c5">V</font> )</span><br/>









<a NAME="E1:62"/>
<font color="Maroon" title="c2">y0</font>,<font color="Maroon" title="c3">y1</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a> 
 
<b>by </b><i><a class="ref" href="borsuk_2.html#D3" title="BORSUK_2:def.3">BORSUK_2:def 3</a></i>;<br/>
<b>hence </b><a NAME="E2:62"/>
( <font color="Maroon" title="c4">R</font>,<font color="Maroon" title="c5">V</font> <a href="borsuk_2.html#R4" title="BORSUK_2:pred.4">are_homotopic</a>  implies  <a href="topalg_1.html#K4" title="TOPALG_1:func.4">pi_1-iso</a> <font color="Maroon" title="c4">R</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="topalg_1.html#K4" title="TOPALG_1:func.4">pi_1-iso</a> <font color="Maroon" title="c5">V</font> )
 <b>by </b><i><a class="ref" href="topalg_1.html#T49" target="_self" title="TOPALG_1:th.49">Th49</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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