On Farthest Points

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Authors

  • G. C. Ahuja
     Department of Mathematics, University of Delhi, Delhi 110007 ,IN
  • T. D. Narang
     Department of Mathematics, University of Delhi, Delhi 110007 ,IN
  • Swaran Trehan
     Department of Mathematics, University of Delhi, Delhi 110007 ,IN

Abstract

Section 2 of this paper deals with the generalizations of a theorem due to Motzkin, Straus and Valentine [7] and a theorem due to V. Klee [4]. Theorem 1 studies the continuity of the farthest point map in a matric space and Theorem 2 establishes that if a compact set in a Frechet space [9] is uniquely remotal with respect to the closure of its convex hull then the set is singleton.

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Published

1975-12-01

How to Cite

Ahuja, G. C., Narang, T. D., & Trehan, S. (1975). On Farthest Points. The Journal of the Indian Mathematical Society, 39(1-4), 293–297. Retrieved from https://informaticsjournals.co.in/index.php/jims/article/view/16654

Issue

Volume 39, Issue 1-4, March-December 1975

Section

Articles

License

Copyright (c) 1975 G. C. Ahuja, T. D. Narang, Swaran Trehan

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

CHENEY, Ward; GOLDSTEIN, A. A., Proximity maps for Convex sets Proc. American Math Soc. 10 (.1959), 448-450.

DAY, M.M., Normed Linear Spaces, Academic Press, New York, 1962.

DUNFORD N; SCHWARTZ J.T., Linear Operators, Part I, Interscience Publishers. New York, 1967.

KLEE, V.L., Convexity of Chebyshev Sets, Math. Ann. 142 (1961) 292-204.

LELEK, A; MYCIELSKI, JAN., On Convex Metric Spaces IV, Fundament Mathematicae, 61 (1967), 171-176.

LIN, BOR-LUH, Distance”Sets in Normed Vector Spaces, Nieuw Archief Voor Wiskunde (3), 14 (1966), 23-30.

MOTZKIN, T.S., STRAUS, E.G., AND VALENTINE, F.A., The Number of Farthest Points, Pacific. J. Math. 3 (1953), 221-232.

NICOLESCU, M., Sur la meilleure approximation d'une function donnee par les fonctions d'une famille donnee, Bui. Fac. Sti. Cernauti, 12 (1938) 120-128.

ROBERTSON; A.P., ROBERTSON, W.J., Topological Vector Spaces, Cambridge University Press, 1966.

SINGER, IVAN, Best Approximation in Normed Linear Spaces by Elements of Linear subspaces, Springer-Verlag Berlin-Heidelberg, 1970.

VAUOHAN, H.E., On Locally Compact Metrisable Spaces, Bull. American Math. Soc, 43 (1937) 532-535.