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## Homework Statement

Prove that if a topological space has a countable base, then all bases contain a subset which is a countable base

## Homework Equations

A base is a subset of the topological space such that all open sets can be constructed from unions and finite intersections of open sets from the base

## The Attempt at a Solution

I'm only a few pages into this chapter, all I learned so far is arbitrary union and finite intersection are closed operations. I have no clue how to construct a countable subset from an arbitrary base, not to mention that it

must be a base by itself. Any help is appreciated