Question

Given a metric space M with metric d, verify that any ε-ball is an open set.

Answer 1

Prove that for any x0€X and any r>O, the open ball Br(xo) is open. My attempt: Let y€Br(x0). By definition, d(y,x0)

Answer 2

Prove that for any x0∈X and any r>0, the open ball Br(xo) is open. My attempt: Let y∈Br(x0). By definition, d(y,x0)<r

Explanation:

Prove that for any x0∈X and any r>0, the open ball Br(xo) is open. My attempt: Let y∈Br(x0). By definition, d(y,x0)<r