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May 13th, 2015, 10:00 AM   #1
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Open sets and closed sets

Example: limited set, but that is neither closed nor open ... ?????
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May 13th, 2015, 10:18 AM   #2
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Limited?
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May 13th, 2015, 10:28 AM   #3
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Probably 'finite'.

What definitions are you using for 'open' and 'closed'?
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July 15th, 2015, 05:31 AM   #4
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More likely "bounded". An example of a bounded set that is neither open nor closed is [0, 1) (in the real numbers with the usual topology).

If Luiz really means "finite" then we cannot use the real numbers with the usual topology- in that space every finite set is closed.

But we can use any set with the "indiscreet topology", in which the only open sets (and so the only closed sets) are the empty set and the entire set itself. Now, a finite proper subset is neither open nor closed.
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