topology : base for an open subset of R^n

From: Will (anarm3_at_yahoo.it)
Date: 03/17/05 

Date: 17 Mar 2005 02:13:46 -0800

I have found:
Let U subset R^n, U open.
Then U has a basis consisting of euclidean balls.

I have understood:

The set of all euclidean balls B_i of R^n such that B_i subset U is a
basis for the topology of U as a subspace in R^n

-in other words-

the set of all euclidean balls B_i subset R^n such that B_i subset U
is a basis for the induced topology on U,

-i.e.-

for all V subset R^n such that V open in R^n, V cap U is the union of
euclidean balls B_i of R^n such that B_i subset U.

Am i right or wrong?
Will