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## Homework Statement

Find a topological space which does not have a countable basis.

## Homework Equations

Definition of basis : A collection of subsets which satisfy:

(i) union of every set equals the whole set

(ii) any element from an intersection of two subsets is contained in another subset which is itself contained in the intersection

## The Attempt at a Solution

I thought I had it nailed, but the solution i came up with was actually an uncountable basis for the standard euclidean topology, which can also have countable bases. So i need to think of a space which cannot have a countable basis.

I started thinking about a space of cantor-like numbers (infinite strings of 1's and 0's) but this is still a subset of the reals! I am stuck please any hints would be a blessing.