Question

4. In lectures, we defined closed subsets of Rn. The definition can be generalized in the following way. Let X be a subset of R". We say that a subset S C X is closed in X if all limit points of S that are in X are also in S. [Any closed subset of Rn is "closed in Rn*) State whether each of the following sets S is closed in X. For cases where X - Rn (including the case n - 1) and S is not closed, find the closure of S TL (a) S- [0, 2], X -F (b) S - (2,5], X -R (c) S = [0.2] U (2,5], X = R (e) S = (-2,0], X = {x E R : |x| < 2} (g) S = {x = (z, y) E X :cos(r) sin(y ) 〉 0}, X = [0, π/2) x (0, π/2) R2. (j) S = {s E R(Q : s2-2), X = [-5,5]

Answer 1

Sİnc

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