Let X be a metric space with distance function d. Is there any condition that ensures that the closures of open balls of X are the closed balls of same center and radius? In R^n with the euclidean metric this is always true. But if we take R^n with the discrete metric, d(x,y) = 1 if x<>y and d(x,y) = 0 if x = y, then this is not true. For example, the open ball centered at 0 and with radius 1 is {0} and its closure is {0}. But the closed ball centered at 0 and with radius 1 is the whole R.
So, I'd like to know if there's a condition, necessary, sufficient or both, that ensures the desired condition in a general metric space.
Thank you
2007-07-26
10:59:22
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4 answers
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asked by
Adrian
1
in
Mathematics