bell-boolean-spaces-machine/structsdef.html at main · pi-base/bell-boolean-spaces-machine · GitHub

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<html><head>
<BASE HREF="http://home.cc.umanitoba.ca/~mbell/structsdef.html">
<title>StructuresDefinitions</title></head><body>
<center><h3>
<a href = http://home.cc.umanitoba.ca/~mbell/instructions.html>Instructions</a>
<br><a href = http://home.cc.umanitoba.ca/~mbell/spacesdef.html>Space Definitions</a>
<br><a href = http://home.cc.umanitoba.ca/~mbell/propsdef.html>Property Definitions</a>
<br><a href = http://www.umanitoba.ca/cgi-bin/math/bell/props.cgi>Return to Property Selection</a>
<br><a href = http://www.umanitoba.ca/cgi-bin/math/bell/structs.cgi>Return to Structure Selection</a>
</h3></center>
<center><h2><b>Structure Definitions</b></h2></center>
<center>An infinite sum of spaces always means the 1 point
compactification of the infinite sum.</center>
<hr>
<dl>
<dt><b>Closed H</b>
<dd>Closed Hereditary
<dt><b>Zeroset H</b>
<dd>Zeroset Hereditary
<dt><b>Reg Closed H</b>
<dd>Regular Closed Hereditary
<dt><b>Clopen H</b>
<dd>Clopen Hereditary
<hr>
<dt><b>Imaging</b>
<dd>Preserved by continuous images
<dt><b>Open Image</b>
<dd>Open Imaging
<dt><b>Irred Image</b>
<dd>Irreducible Imaging
<dt><b>Simple Image</b>
<dd>Simple Imaging (preserved by collapsing one closed set to a point)
<dt><b>Retract</b>
<dd>Preserved by retractions
<hr>
<dt><b>Multiplicive</b>
<dd>If one factor has the property, then the product has the property.
<dt><b>Productive</b>
<dd>If all factors have the property, then the product has the property.
<dt><b>C Productive</b>
<dd>C Productive
<dt><b>W Productive</b>
<dd>W Productive
<dt><b>2 Productive</b>
<dd>2 Productive
<hr>
<dt><b>Summable</b>
<dd>If all summands have the property, then the sum has the property.
<dt><b>C Summable</b>
<dd>C Summable
<dt><b>W Summable</b>
<dd>W Summable
<dt><b>2 Summable</b>
<dd>2 Summable
<hr>
<dt><b>To Hyper</b>
<dd>If a space has the property, then its hyperspace has the property.
<dt><b>To Mul 2^W</b>
<dd>If X has the property, then X x 2^W has the property.
<dt><b>To Add 1</b>
<dd>If X has the property, then X + 1 has the property.
<hr>
<dt><b>Closed E(xtendible)</b>
<dd>If a closed subspace has the property, then the space has the property.
<dt><b>Zeroset E</b>
<dd>If a zeroset has the property, then the space has the property.
<dt><b>Reg Closed E</b>
<dd>If a regular closed subspace has the property, then the space has the property.
<dt><b>Clopen E</b>
<dd>If a clopen subspace has the property, then the space has the property.
<hr>
<dt><b>PreImaging</b>
<dd>Preserved by continuous preimages.
<dt><b>PreOpenImage</b>
<dd>Preserved by continuous open preimages.
<dt><b>PreIrrdImage</b>
<dd>Preserved by continuous irreducible preimages.
<dt><b>PreSimpImage</b>
<dd>Preserved by continuous simple preimages.
<dt><b>PreRetract</b>
<dd>If a retract of the space has the property, then the space has the property.
<hr>
<dt><b>Projectable</b>
<dd>If a product of spaces has the property, then all factors have the
property.
<dt><b>Factorable</b>
<dd>If a product of spaces has the property, then at least one of the
factors has the property.
<dt><b>C Factorable</b>
<dd>If a product of at most C spaces has the property, then at least one of the
factors has the property.
<dt><b>W Factorable</b>
<dd>If a product of at most W spaces has the property, then at least one of the
factors has the property.
<dt><b>2 Factorable</b>
<dd>If a product of 2 spaces has the property, then at least one of the
factors has the property.
<hr>
<dt><b>Prime</b>
<dd>If a sum of spaces has the property, then at least one of the
summands has the property.
<dt><b>C Prime</b>
<dd>If a sum of at most C spaces has the property, then at least one of the
summands has the property.
<dt><b>W Prime</b>
<dd>If a sum of at most W spaces has the property, then at least one of the
summands has the property.
<dt><b>2 Prime</b>
<dd>If a sum of 2 spaces has the property, then at least one of the
summands has the property.
<hr>
<dt><b>From Hyper</b>
<dd>If the hyperspace has the property, then the space has the property.
<dt><b>From Mul 2^W</b>
<dd>If X x 2^W has the property, then X has the property.
<dt><b>From Add 1</b>
<dd>If X + 1 has the property, then X has the property.
</dl>
<center><h3>
<a href = http://home.cc.umanitoba.ca/~mbell/instructions.html>Instructions</a>
<br><a href = http://home.cc.umanitoba.ca/~mbell/spacesdef.html>Space Definitions</a>
<br><a href = http://home.cc.umanitoba.ca/~mbell/propsdef.html>Property Definitions</a>
<br><a href = http://www.umanitoba.ca/cgi-bin/math/bell/props.cgi>Return to Property Selection</a>
<br><a href = http://www.umanitoba.ca/cgi-bin/math/bell/structs.cgi>Return to Structure Selection</a>
</h3></center>
</body>
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