Open and Closed Sets
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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 E R : x > 0}
(d) {0,1) = {x E R : 0 < x less the or equal to 1}
(e) {1 + 1/4 + 1/9 + ... + 1/n^2 : n E N}
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a) Q is neither open nor closed
b) N is neither open nor closed
c) Take any point x contained in R. Clearly, any neighborhood of x consists of real numbers, and hence is ...
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