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<b>let </b><font color="Maroon" title="c1">T</font> be   <a href="t_0topsp.html#NM1" title="T_0TOPSP:NM.1">T_0-TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">T</font> is <a href="waybel18.html#V2" title="WAYBEL18:attr.2">injective</a> implies  ex <font color="Olive" title="b1">M</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <font color="Maroon" title="c1">T</font> <a href="waybel18.html#R1" title="WAYBEL18:pred.1">is_Retract_of</a>  <a href="waybel18.html#K3" title="WAYBEL18:func.3">product</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">M</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <a href="waybel18.html#K9" title="WAYBEL18:func.9">Sierpinski_Space</a> </span>)</span> )</span><br/>

<b>assume </b><a NAME="E1:49"/><i><font color="Green" title="E22">A1</font></i>: 
<font color="Maroon" title="c1">T</font> is <a href="waybel18.html#V2" title="WAYBEL18:attr.2">injective</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">M</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <font color="Maroon" title="c1">T</font> <a href="waybel18.html#R1" title="WAYBEL18:pred.1">is_Retract_of</a>  <a href="waybel18.html#K3" title="WAYBEL18:func.3">product</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">M</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <a href="waybel18.html#K9" title="WAYBEL18:func.9">Sierpinski_Space</a> </span>)</span></span><br/>

<b>consider </b><font color="Maroon" title="c2">M</font> being  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> , <font color="Maroon" title="c3">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">T</font>,<span class="p1">(<span class="default"><a href="waybel18.html#K3" title="WAYBEL18:func.3">product</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">M</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <a href="waybel18.html#K9" title="WAYBEL18:func.9">Sierpinski_Space</a> </span>)</span></span>)</span><b> such that </b><br/><a NAME="E3:49"/><i><font color="Green" title="E23">A2</font></i>: 
 <a href="waybel18.html#K8" title="WAYBEL18:func.8">corestr</a> <font color="Maroon" title="c3">f</font> <a href="tops_2.html#NR1" title="TOPS_2:NR.1">is_homeomorphism</a> 
 <b>by </b><i><a class="ref" href="waybel18.html#T19" target="_self" title="WAYBEL18:th.19">Th19</a></i>;<br/>
<b>thus </b><a NAME="E4:49"/>
 ex <font color="Olive" title="b1">M</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <font color="Maroon" title="c1">T</font> <a href="waybel18.html#R1" title="WAYBEL18:pred.1">is_Retract_of</a>  <a href="waybel18.html#K3" title="WAYBEL18:func.3">product</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">M</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <a href="waybel18.html#K9" title="WAYBEL18:func.9">Sierpinski_Space</a> </span>)</span>
 <b>by </b><i><a class="txt" href="waybel18.html#E1:49"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="waybel18.html#E3:49"><i><font color="Green" title="E23">A2</font></i></a>, <a class="ref" href="waybel18.html#T12" target="_self" title="WAYBEL18:th.12">Th12</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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