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 May 13th, 2015, 10:00 AM #1 Member   Joined: Mar 2015 From: Brasil Posts: 90 Thanks: 4 Open sets and closed sets Example: limited set, but that is neither closed nor open ... ?????
 May 13th, 2015, 10:18 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Limited?
 May 13th, 2015, 10:28 AM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,675 Thanks: 2654 Math Focus: Mainly analysis and algebra Probably 'finite'. What definitions are you using for 'open' and 'closed'?
 July 15th, 2015, 05:31 AM #4 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 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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