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ISSN : 1226-0657

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Vol.9 No.1
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ON FARTHEST POINTS IN METRIC SPACES

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2002, v.9 no.1, pp.1-7
Narang, T.D.
Narang,, T. (2002). ON FARTHEST POINTS IN METRIC SPACES. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 9(1), 1-7.
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Abstract

For A bounded subset G of a metric Space (X,d) and <TEX>$\chi \in X$</TEX>, let <TEX>$f_{G}$</TEX> be the real-valued function on X defined by <TEX>$f_{G}$</TEX>(<TEX>$\chi$</TEX>)=sup{<TEX>$d (\chi, g)\in:G$</TEX>}, and <TEX>$F(G,\chi)$</TEX>={<TEX>$z \in X:sup_{g \in G}d(g,z)=sup_{g \in G}d(g,\chi)+d(\chi,z)$</TEX>}. In this paper we discuss some properties of the map <TEX>$f_G$</TEX> and of the set <TEX>$ F(G, \chi)$</TEX> in convex metric spaces. A sufficient condition for an element of a convex metric space X to lie in <TEX>$ F(G, \chi)$</TEX> is also given in this pope.

keywords
fathet point, farthest point map, remotal set, uniquely remotal set, nearly compact set, convex metric space

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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