Question

Prove that in a metric space, every sphere is an open set​

Answer 1

Answer:

We say that a subset U of X is open if, given any point x ∞ U, there exists r > 0 and an open ball B(x, r) such that B(x, r) ™ U. ... Theorem A1 Let (X, d) be a metric space. Then any open ball is an open set.