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

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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[3]	O. Kopecek, |End A| = |\Con A| = |Sub A| = 2A for any uncountable 1-unary algebra A, Algebra Universalis 16 (1983), 312-317.
[4]	O. Kopecek, A note on some cardinal functions on unary algebras, Contributions to General Algebra 2 (1983), 221-227.
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[7]	A.K. Steiner, The lattice of topologies: Structure and complementation, Trans. Amer. Math. Soc. 122 (1966), 379-398.

Received 27 November 2000
Revised 14 December 2001