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December 8th, 2010, 02:42 PM   #1
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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?
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December 8th, 2010, 08:01 PM   #2
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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.
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December 9th, 2010, 04:10 PM   #3
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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.
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