My Math Forum Open Balls...

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 December 8th, 2010, 02:42 PM #1 Member   Joined: Jan 2008 Posts: 34 Thanks: 0 Open Balls... D(X,Y) = |x1-y1|+|x2-y2|, ?X,Y?R^2 is a metric on the plane of reals How does one show that the family of all open balls in the metric 'D' is a basis for the regular topology on R^2?
 December 8th, 2010, 08:01 PM #2 Newbie   Joined: Nov 2009 Posts: 3 Thanks: 0 Re: Open Balls... To show that two bases A and B generate the same topology on X, you show that for a given basis element M of A and point x in M, there exists a basis element N of B such that x is in N and N is a subset of M. Then you do the same thing in the other direction.
 December 9th, 2010, 04:10 PM #3 Member   Joined: Jan 2008 Posts: 34 Thanks: 0 Re: Open Balls... I have only one basis, and I need to show that it is indeed a basis... could you be more specific? maybe wrt the objects I mentioned? I'm not very fluent in topology proofs/jargon.

 Tags balls, open

### show that the subsets of the plane are open A={(x,y) | -1 < x < 1, -1

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