MATHEMATICA BOHEMICA, Vol. 127, No. 3, pp. 437-448 (2002)

A Galois connection between distance functions and inequality relations

Arpad Szaz

Arpad Szaz, Institute of Mathematics and Informatics, University of Debrecen, H-4010 Debrecen, Pf. 12, Hungary, e-mail: szaz@math.klte.hu

Abstract: Following the ideas of R. DeMarr, we establish a Galois connection between distance functions on a set $S$ and inequality relations on $X_{S}=S \times \Bbb R$. Moreover, we also investigate a relationship between the functions of $S$ and $X_{S}$. \endabstract

Keywords: distance functions and inequality relations, closure operators and Galois connections, Lipschitz and monotone functions, fixed points

Classification (MSC2000): 54E25, 06A06, 47H10, 06A15

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