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Topic: Extension of the Euclidean Metric to Subsets
Replies: 6   Last Post: Sep 16, 2005 11:09 AM

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Maury Barbato

Posts: 572
From: University Federico II of Naples
Registered: 3/15/05
Extension of the Euclidean Metric to Subsets
Posted: Sep 15, 2005 11:59 AM
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Hello,
the problem which I'm thinking about is the following:
let P(R^n) the power set of R^n (that is the set of all the subsets of R^n).
Does there exist a metric m on P(R^n) such that for every x,y in R^n we have m({x},{y})=d(x,y), where d is the usual euclidean metric of R^n?
For compact subsets we have the Hausdorff metric, which has this property.
For all subsets the answer is negative, I think.
What is your opinion?
Maury

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