Cardinalities of lattices of topologies of unars and some related topics

Anna Kartashova

Discussiones Mathematicae - General Algebra and Applications (2001)

  • Volume: 21, Issue: 2, page 129-137
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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Anna Kartashova. "Cardinalities of lattices of topologies of unars and some related topics." Discussiones Mathematicae - General Algebra and Applications 21.2 (2001): 129-137. <http://eudml.org/doc/287604>.

@article{AnnaKartashova2001,
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.},
author = {Anna Kartashova},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {unar; lattice of topologies; lattice of congruences; lattices of topologies; uncountable unars; congruence lattice},
language = {eng},
number = {2},
pages = {129-137},
title = {Cardinalities of lattices of topologies of unars and some related topics},
url = {http://eudml.org/doc/287604},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Anna Kartashova
TI - Cardinalities of lattices of topologies of unars and some related topics
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2001
VL - 21
IS - 2
SP - 129
EP - 137
AB - 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.
LA - eng
KW - unar; lattice of topologies; lattice of congruences; lattices of topologies; uncountable unars; congruence lattice
UR - http://eudml.org/doc/287604
ER -

References

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  1. [1] D.P. Egorova, Unars with congruence lattices of special kinds (Russian), Issledovania po algebre (Saratov) 5 (1977), 3-19. 
  2. [2] A.V. Kartashova, About some properties of lattices of topologies of algebras (Russian), Dep. no. 404 VINITI, 21.02.00. Zbl1241.08003
  3. [3] O. Kopecek, | E n d A | = | C o n A | = | S u b A | = 2 A for any uncountable 1-unary algebra A, Algebra Universalis 16 (1983), 312-317. 
  4. [4] O. Kopecek, A note on some cardinal functions on unary algebras, Contributions to General Algebra 2 (1983), 221-227. Zbl0531.08003
  5. [5] S.D. Orlov, About the lattice of possible topologies (Russian), Uporadocennye mnozestva i resetki (Saratov) 2 (1974), 68-71. 
  6. [6] L.A. Skorniakov, Unars, Colloq. Math. Soc. J. Bolyai, vol. 29 ('Universal Algebra'), North-Holland, Amsterdam 1982, 735-743. 
  7. [7] A.K. Steiner, The lattice of topologies: Structure and complementation, Trans. Amer. Math. Soc. 122 (1966), 379-398. Zbl0139.15905

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