(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant 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

3. 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

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# Homework Help: Proof about countable base of topological space

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