Question

show that every matric space is a normal space as well as a regular space​

Answer 1

Step-by-step explanation:

We can show that all metric spaces are normal. Naturally, we wish to know whether all normal spaces are metrizable. ... A topological space X is first countable if for each point p ∈ X, there exists a countable family of open sets {Un}n∈N containing p such that for each open set V p, there exists an n such that Un ⊂ V .