Problems on open and closed sets

Question

Questions:

Open and Closed Sets

Decide whether the following sets are open, closes or neither. If a set is not open, find a point in the set for which there is no E-neighborhood contained in the set. If a set is not closed, find a limit point that is not contained in the set.

(a) Q

(b) N

(c) {x∈R : x > 0}

(d) {0,1) = {x ∈ R : 0 < x ≤1}

(e) {1 + 1/4 + 1/9 + ... + 1/n² : n∈N}