June 20th, 2016, 01:38 PM  #1  
Newbie Joined: Jun 2016 From: NY Posts: 1 Thanks: 0  Connectedness  Relatively Close Quote:
Isn't it that the intersection of (1/2, 3/2) and A is again [0, 1] is a closed subset of A? Wonder if someone could help point that out to me. Thank you!!  
June 22nd, 2016, 05:49 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
Given A a subset of X, a set U is "open in A" (or "relative to A") if and only if U is equal to the intersection of an open subset of X with A. Similarly, U is "closed in A" if and only if U is equal to the intersection of a closed subset of X with A. (Sometimes those are used as the definitions of "open in A" and "closed in A".) 

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