Discussiones Mathematicae General Algebra and Applications 21(2) (2001) 129-137
doi: 10.7151/dmgaa.1033

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CARDINALITIES OF LATTICES OF TOPOLOGIES OF UNARS AND SOME RELATED TOPICS

Anna Kartashova

Department of Algebra and Geometry
Volgograd Pedagogical University
Eletskaya 7-177, 400120 Volgograd, Russia
e-mail:
kvk@vspu.ru

Abstract

In this paper we find cardinalities of lattices of topologies of uncountable unars and show that the lattice of topologies of a unar cannor be countably infinite. It is proved that under some finiteness conditions the lattice of topologies of a unar is finite. Furthermore, the relations between the lattice of topologies of an arbitrary unar and its congruence lattice are established.

Keywords: unar, lattice of topologies, lattice of congruences.

2000 Mathematics Subject Classification:  08A60, 22A30, 08A30.

References

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Received 27 November 2000
Revised 14 December 2001