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
x_{1}, x_{2} Î X we have
x_{1} £ φ(x_{2})
if and only if
f(x_{1}) £ f(x_{2});
(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 |