Assignment:
For the following, I'm trying to decide (with proof) if A is a closed subset of Y with respect to the topology, T
(i) Y = N, T is the finite complement topology, A = {n e N | n^2 - 2011n+1 < 0}.
(ii) Y = R, T is the usual topology, A is the set of irrational numbers between 0 and 1.
(iii) Y = R, T is the discrete topology, A is the set consisting of all the numbers that do not have 5, 3, or 2 in any of their decimal expansions.
Provide complete and step by step solution for the question and show calculations and use formulas.