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Posted: Thu May 05, 2022 6:35 pm
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Let X = R and T:= {0} U {(a, ∞o)|a € R} U {R}.
Let (X,T) be as in the previous problem. (1) For any A≤R, describe the closure of A with respect to T. (2) Show that there are subsets of R that are compact (every open cover of them has a finite subcover), but not closed.
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Let (X,T) be as in the previous problem. (1) For any A≤R, describe the closure of A with respect to T. (2) Show that there are subsets of R that are compact (every open cover of them has a finite subcover), but not closed.