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.

Decomposition of topologies on lattices and hyperspaces

Costantini C., Vitolo P.

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AbstractThe notion of decomposable topology is introduced in a partially ordered set and, in particular, in the lattice C(X) of all closed subsets (ordered by reverse inclusion) of a topological space X, which is also called the hyperspace of X. This notion is closely related to the concepts, defined in the same framework, of lower, upper and strong upper topology.We investigate decomposability and unique decomposability of the main hyperspace topologies, and of topologies which are...