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science forum beginner

Joined: 11 Oct 2005
Posts: 17

Posted: Thu Jul 13, 2006 4:47 pm    Post subject: distance between sets

Hello

Suppose X and Y are two closed, bounded and convex sets.

I need a metric such that d(X,Y) = 0 iff X=Y.

for example the Hausdorff metric
(http://planetmath.org/encyclopedia/HausdorffMetric.html) can help
me.

Is there any other "popular" metric that has that property?

Diego
step_y@yahoo.com
science forum beginner

Joined: 13 Jul 2006
Posts: 1

Posted: Thu Jul 13, 2006 6:16 pm    Post subject: Re: distance between sets

sure sounds pretty interesting

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 Quote: Hello Suppose X and Y are two closed, bounded and convex sets. I need a metric such that d(X,Y) = 0 iff X=Y. for example the Hausdorff metric (http://planetmath.org/encyclopedia/HausdorffMetric.html) can help me. Is there any other "popular" metric that has that property? thanks a lot for your answer Diego
Dave L. Renfro
science forum Guru

Joined: 29 Apr 2005
Posts: 570

Posted: Thu Jul 13, 2006 6:53 pm    Post subject: Re: distance between sets

 Quote: Suppose X and Y are two closed, bounded and convex sets. I need a metric such that d(X,Y) = 0 iff X=Y. for example the Hausdorff metric (http://planetmath.org/encyclopedia/HausdorffMetric.html) can help me. Is there any other "popular" metric that has that property?

?? *Every* metric satisfies d(X,Y) = 0 iff X=Y.
(Well, maybe not in general relativity ...)

Nevertheless, perhaps some of the following could be useful:

http://www.fas.org/sgp/othergov/doe/lanl/pubs/00285752.pdf

http://tinyurl.com/hdqzf

http://www.maths.warwick.ac.uk/~jcr/re/usc.pdf [see p. 3]

http://www.sztaki.hu/~szatmari/thesis.pdf

Dave L. Renfro

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