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a) a closed set S[itex]\subset[/itex]ℝ and a continous function f: ℝ-->ℝ such that f(S) is not closed;

b) an open set U[itex]\subset[/itex]ℝ and a continous function f: ℝ-->ℝ such that f(U) is not open

Solution:

a) e^x b) x^2

here's my problem, this is what was given in the solutions, but I don't see how the two respective answers are an open and closed set. The continuity isn't a problem, but the open and close concept is bugging me. How is e^x closed if I can pick any value of "x"? Like my interpretation of closed was any stated interval where you may have to say [a,b] is the interval also topologically I viewed it as the closure = union of the interior points an boundary points.