Metrizable implies first-countable

This article gives the statement and possibly, proof, of an implication relation between two topological space properties. That is, it states that every topological space satisfying the first topological space property (i.e., metrizable space) must also satisfy the second topological space property (i.e., first-countable space)
View all topological space property implications | View all topological space property non-implications
Get more facts about metrizable space|Get more facts about first-countable space

Statement

Any metrizable space is a first-countable space.

Related facts

• First-countable implies compactly generated

Proof

Fill this in later