Topological Bases: Are Two Definitions Equivalent?

[ehrenfest]

Homework Statement

I have seen two definitions for the topology generated by a basis set:
one here http://books.google.com/books?id=9c...j81v&sig=nNFNyWXorlwCQ8WCwQBDTuI9HUc#PPA22,M1
and the other one is
a set U is open if for every x in U, there is a basis element Bi with x in Bi in U

Are they equivalent?

Homework Equations

The Attempt at a Solution

 

[morphism]

Yes. Try proving this yourself and post back if you have problems.