Displaying similar documents to “Generating methods for principal topologies on bounded lattices”

A principal topology obtained from uninorms

Funda Karaçal, Tuncay Köroğlu (2022)

Kybernetika

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We obtain a principal topology and some related results. We also give some hints of possible applications. Some mathematical systems are both lattice and topological space. We show that a topology defined on the any bounded lattice is definable in terms of uninorms. Also, we see that these topologies satisfy the condition of the principal topology. These topologies can not be metrizable except for the discrete metric case. We show an equivalence relation on the class of uninorms on a...

Cardinalities of lattices of topologies of unars and some related topics

Anna Kartashova (2001)

Discussiones Mathematicae - General Algebra and Applications

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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.