Just wondering if someone could help me with this problem.

For two disjoint compact subsets of R^n, show that there is a minimum positive distance between the points of each set.

Much appreciated!

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- April 23rd 2008, 02:39 AMgasbasisHelp with proof (sets)
Just wondering if someone could help me with this problem.

For two disjoint compact subsets of R^n, show that there is a minimum positive distance between the points of each set.

Much appreciated! - April 23rd 2008, 04:47 AMPlato
Here is an outline.

Suppose that the two subsets are A & B and that D(A,B)=0.

Use the definition of*distance between sets*to get a sequence of distinct points in A that must converge to a point in B. That happens due to compactness. That will give you a contradiction. - April 23rd 2008, 10:58 AMThePerfectHacker
We can generalize this. If A is compact and B is closed subsets of R^n then d(A,B) > 0

- April 23rd 2008, 05:14 PMgasbasis