10-327/Separation Axioms: Difference between revisions
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Since I made a mistake with the pathes and these files will likely be deleted or moved, I'm including a link to the [http://christopherolah.wordpress.com/2010/08/14/separation-axiom-visualisations/ |
Since I made a mistake with the pathes and these files will likely be deleted or moved, I'm including a link to the [http://christopherolah.wordpress.com/2010/08/14/separation-axiom-visualisations/ original source on my blog]. |
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The separation axioms along with other properties form a network of implications: |
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[[Image:10-327-separation-axioms-graph.png|450px]] |
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It's interesting to note that paracompactness (every open cover has a subcover such that every point has a neighbourhood that intersects finitely many elements) will suffice in place of compactness. |
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Latest revision as of 15:57, 19 December 2010
T0:
T1:
T2:
T3:
T3.5:
T4:
T4.5:
Since I made a mistake with the pathes and these files will likely be deleted or moved, I'm including a link to the original source on my blog.
The separation axioms along with other properties form a network of implications:
It's interesting to note that paracompactness (every open cover has a subcover such that every point has a neighbourhood that intersects finitely many elements) will suffice in place of compactness.
