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On Exposed and Farthest Points in Normed Linear Spaces

Published online by Cambridge University Press:  09 April 2009

M. Edelstein  and
J. E. Lewis
M. Edelstein
Affiliation:
Dalhousie University Halifax, Nova Scotia
J. E. Lewis
Affiliation:
Dalhousie University Halifax, Nova Scotia
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Let S be a nonempty subset of a normed linear space E. A point s0 of S is called a farthest point if for some x ∈ E, . The set of all farthest points of S will be denoted far (S). If S is compact, the continuity of distance from a point x of E implies that far (S) is nonempty.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 12 , Issue 3 , August 1971 , pp. 301 - 308
Copyright
Copyright © Australian Mathematical Society 1971

References

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