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A characterization of 1-, 2-, 3-, 4-homomorphisms of ordered sets

Radomír Halaš, Daniel Hort (2003)

Czechoslovak Mathematical Journal

We characterize totally ordered sets within the class of all ordered sets containing at least four-element chains. We use a simple relationship between their isotone transformations and the so called 1-endomorphism which is introduced in the paper. Later we describe 1-, 2-, 3-, 4-homomorphisms of ordered sets in the language of super strong mappings.

A characterization of finite Stone pseudocomplemented ordered sets

Radomír Halaš (1996)

Mathematica Bohemica

A distributive pseudocomplemented set S [2] is called Stone if for all a S the condition L U ( a * , a * * ) = S holds. It is shown that in a finite case S is Stone iff the join of all distinct minimal prime ideals of S is equal to S .

Binary and ternary relations

Vítězslav Novák, Miroslav Novotný (1992)

Mathematica Bohemica

Two operators are constructed which make it possible to transform ternary relations into binary relations defined on binary relations and vice versa. A possible graphical representation of ternary relations is described.

Cardinal and ordinal arithmetics of n -ary relational systems and n -ary ordered sets

Jiří Karásek (1998)

Mathematica Bohemica

The aim of this paper is to define and study cardinal (direct) and ordinal operations of addition, multiplication, and exponentiation for n -ary relational systems. n -ary ordered sets are defined as special n -ary relational systems by means of properties that seem to suitably generalize reflexivity, antisymmetry, and transitivity from the case of n = 2 or 3. The class of n -ary ordered sets is then closed under the cardinal and ordinal operations.

Convex isomorphisms of directed multilattices

Ján Jakubík, Mária Csontóová (1993)

Mathematica Bohemica

By applying the solution of the internal direct product decomposition we investigate the relations between convex isomorphisms and direct product decompositions of directed multilattices.

Finite topological spaces.

Juan A. Navarro González (1990)

Extracta Mathematicae

We show that the study of topological T0-spaces with a finite number of points agrees essentially with the study of polyhedra, by means of the geometric realization of finite spaces. In this paper all topological spaces are assumed to be T0.

Fixed points theorems of non-expanding fuzzy multifunctions

Abdelkader Stouti (2005)

Archivum Mathematicum

We prove the existence of a fixed point of non-expanding fuzzy multifunctions in α -fuzzy preordered sets. Furthermore, we establish the existence of least and minimal fixed points of non-expanding fuzzy multifunctions in α -fuzzy ordered sets.

Induced pseudoorders

Ivan Chajda, Miroslav Haviar (1991)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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