- #1
sunjin09
- 312
- 0
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