Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 17, No. 2, pp. 61-69 (2001)

Characterizations of effective sets and nonexpansive multipliers in conditionally complete and infinitely distributive partially ordered sets

István Kovács and Árpád Száz

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

Abstract: First, we establish a useful characterization of effective sets in conditionally complete partially ordered sets. Then, we prove that each maximal nonexpansive partial multiplier on a conditionally complete and infinitely distributive partially ordered set with upper bounded centre is inner. Finally, we show that some analogous results hold for $T_1$-families of sets partially ordered by inclusion.

Keywords: Partially ordered sets, conditional completeness and infinite distributivity, effective sets and nonexpansive multipliers

Classification (MSC2000): 06A06; 06A12, 20M14, 20M15

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