Re: basic question about metric space... is a distance metric continuous function?

On Tue, 6 Dec 2005, comtech wrote:
>
> I have a basic question about metric space... is a distance metric
> continuous function?
>
> I mean the distance function in a metric space itself,
> say the metric space is (M, d),
> let d be defined as d: M x M -> R
>
> is this function "d" neccessarily continuous? Under what condition is
> it continuous?
>
As M has the topology generated by the open balls,
d is Lipschitz continuous.

.

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