Sets associated with the farthest point problem |
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| Authors: | Duane Detemple Jack Robertson |
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| Institution: | (1) Department of Pure and Applied Mathematics, Washington State University, 99164-3113 Pullman, Washington, U.S.A. |
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| Abstract: | LetS be a convex compact set in a normed linear spaceX. For each cardinal numbern, defineS
n = {x  X:x has exactlyn farthest points inS} andT
n = 
k n
S
k. It is shown that ifX =E thenT
3 is countable andT
2 is contractible to a point. Properties of associated level curves are given. |
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| Keywords: | 52A10 52A20 |
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