Metric Spaces | Lecture 39 | A Set is Open iff it is a Union of Open Balls

A Set is Open iff it is a Union of Open Balls

[bismitapegu]

Thank you sir I able to understand nicely now after watching ur vedio....

[erkinrahmonov]

It's great. Prove that the set M={f: f(t)<g(t)} is an open set for the corresponding function C[a;b] in the metric space C[a;b]. Help

[tatihveudmia]

Prove that using Baire's theorem that any compact topological space is a set of second category in itself.

[-pinkidhobi]

2. Let (X, d) be a metric space and x, y ∈ X, r, s > 0. If B(x, r) = B(y, s),
then
How to solve this question