In a metric space (X, d) the closed ball of radius ε > 0 about the point x in X is the set
B(x; ε) = {y ∈ X: d(x,y)< ε}.
(a) Prove that B(x; ε) is a closed set.
(b) Prove that cl N(x; ε) ⊆ B(x; ε).
(c) Find an example of a metric space (X, d), a point x ∈ X, and a radius ε > 0 such that cl N(x; ε) ≠ B(x; ε).
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.