10-327/Separation Axioms: Difference between revisions
From Drorbn
Jump to navigationJump to search
(Created, added pictures. Yay!) |
No edit summary |
||
| (5 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
T0: |
T0: |
||
[[Image: |
[[Image:T0SA.png|250px]] |
||
T1: |
T1: |
||
[[Image: |
[[Image:T1SA.png|250px]] |
||
T2: |
T2: |
||
[[Image: |
[[Image:T2SA.png|250px]] |
||
T3: |
T3: |
||
[[Image: |
[[Image:T3SA.png|250px]] |
||
T3.5: |
T3.5: |
||
[[Image: |
[[Image:T35SA.png|250px]] |
||
T4: |
T4: |
||
[[Image: |
[[Image:T4SA.png|250px]] |
||
T4.5: |
T4.5: |
||
[[Image: |
[[Image:T45SA.png|250px]] |
||
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]. |
|||
The separation axioms along with other properties form a network of implications: |
|||
[[Image:10-327-separation-axioms-graph.png|450px]] |
|||
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. |
|||
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.
