Question
Check whether the following sets are open or closed or neither:
(i)
(ii)
Answer :
Word Count : 212
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Consider the first set: [ A = { 3n : n \in \mathbb{N} }. ] This is a set of discrete points ({3, 6, 9, 12, \dots}) in (\mathbb{R}). In the real numbers, an open set requires that for each point there exists an interval around it entirely contained in the set. For any (3n \in A), any interval around (3n) will contain non-multiples of 3, which are not in
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