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 Post subject: point-set topology --- interior and closurePosted: Mon, 16 Feb 2009 18:27:13 UTC
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This question is probably familiar to many, but it is a fun problem.

How many distinct sets are possible using closure and interior, starting from some subset A of some topological space X? In other words, how many distinct subsets can there be in the sequence

For each possibility, give an example of the pair (X,A).

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 Post subject: Posted: Mon, 16 Feb 2009 22:20:43 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
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Location: Austin, TX

Spoiler:
14.

Now can anyone exhibit a set which achieves all of them?

Hint 1:
Spoiler:

Hint 2:
Spoiler:
Be creative with the way you choose the endpoints of your interval(s)

Hint 3: (pretty big)
Spoiler:
Be creative with the connectivity of your set

Hint 4: (BIG)
Spoiler:
Use dense subsets well
.

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 Post subject: Posted: Mon, 16 Feb 2009 22:56:44 UTC
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Shadow --- Taking complement is not allowed here!

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 Post subject: Posted: Mon, 16 Feb 2009 23:12:19 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
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Location: Austin, TX

.
.
.

Well, that's what I get for not reading carefully . Thanks outermeasure!

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