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 PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2009, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |