Topology question - helpdrowning student

[zilla]

If X is a T₁, 1st countable topological space and x is a limit point of A in X, then there exists a sequence {b_n} in A whose limit is x.


(I'm doing this class through independent study, and in this last session the prof decided we hadn't covered enough in the semester (even though we've gone through his syllabus), so he threw a bunch of concepts at me that I'd never heard of, including the T1 and "1st countable" descriptives. He didn't bother telling me what they mean when I asked - he just said we had more to cover, so I'm at a loss. I really need some help here.)

 

[VeeEight]

Look up the definition of a first countable space, if you haven't already, and consider a countable basis at x. Use this to construct your sequence.