Vol. LXXVIII, 1 (2009)
p. 1 - 21

Galois-type connections and closure operations
on preordered sets

Á. Száz

Received: March 10, 2007;   Revised: January 15, 2009;   Accepted: January 16, 2009

Abstract.   For a function f of one preordered set X to another Y, we shall establish several consequences of the following two definitions:
(a)  f is increasingly φ-regular, for some function φ of X to itself, if for any x1, x2 Î X we have   x1 £ φ(x2)   if and only if   f(x1) £ f(x2);
(b)  f is increasingly g-normal, for some function g of Y to X, if for any x Î X and y Î Y we have  f(x) £ y  if and only  if  x £ g(y).
These definitions have been mainly suggested to us by a recent theory of relators (families of relations) worked out by Á. Száz and G. Pataki and the extensive literature on Galois connections and residuated mappings.

Keywords:  Preordered sets; Galois connections (residuated mappings); closure operations; generalized uniformities (relational systems)  

AMS Subject classification: Primary:  06A06, 06A15   Secondary: 04A05, 54E15

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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

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