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𝒵 -distributive function lattices

Marcel Erné (2013)

Mathematica Bohemica

It is known that for a nonempty topological space X and a nonsingleton complete lattice Y endowed with the Scott topology, the partially ordered set [ X , Y ] of all continuous functions from X into Y is a continuous lattice if and only if both Y and the open set lattice 𝒪 X are continuous lattices. This result extends to certain classes of 𝒵 -distributive lattices, where 𝒵 is a subset system replacing the system 𝒟 of all directed subsets (for which the 𝒟 -distributive complete lattices are just the continuous...

A new look at pointfree metrization theorems

Bernhard Banaschewski, Aleš Pultr (1998)

Commentationes Mathematicae Universitatis Carolinae

We present a unified treatment of pointfree metrization theorems based on an analysis of special properties of bases. It essentially covers all the facts concerning metrization from Engelking [1] which make pointfree sense. With one exception, where the generalization is shown to be false, all the theorems extend to the general pointfree context.

A sufficient condition of full normality

Tomáš Kaiser (1996)

Commentationes Mathematicae Universitatis Carolinae

We present a direct constructive proof of full normality for a class of spaces (locales) that includes, among others, all metrizable ones.

Degrees of compatible L -subsets and compatible mappings

Fu Gui Shi, Yan Sun (2024)

Kybernetika

Based on a completely distributive lattice L , degrees of compatible L -subsets and compatible mappings are introduced in an L -approximation space and their characterizations are given by four kinds of cut sets of L -subsets and L -equivalences, respectively. Besides, some characterizations of compatible mappings and compatible degrees of mappings are given by compatible L -subsets and compatible degrees of L -subsets. Finally, the notion of complete L -sublattices is introduced and it is shown that the...

Direct product decompositions of infinitely distributive lattices

Ján Jakubík (2000)

Mathematica Bohemica

Let α be an infinite cardinal. Let 𝒯 α be the class of all lattices which are conditionally α -complete and infinitely distributive. We denote by 𝒯 σ ' the class of all lattices X such that X is infinitely distributive, σ -complete and has the least element. In this paper we deal with direct factors of lattices belonging to 𝒯 α . As an application, we prove a result of Cantor-Bernstein type for lattices belonging to the class 𝒯 σ ' .

Duality for CCD lattices.

Marmolejo, Francisco, Rosebrugh, Robert, Wood, R.J. (2009)

Theory and Applications of Categories [electronic only]

Extensions of fuzzy connectives on ACDL

Hui Liu, Bin Zhao (2019)

Kybernetika

The main goal of this paper is to construct fuzzy connectives on algebraic completely distributive lattice(ACDL) by means of extending fuzzy connectives on the set of completely join-prime elements or on the set of completely meet-prime elements, and discuss some properties of the new fuzzy connectives. Firstly, we present the methods to construct t-norms, t-conorms, fuzzy negations valued on ACDL and discuss whether De Morgan triple will be kept. Then we put forward two ways to extend fuzzy implications...

Higher degrees of distributivity in M V -algebras

Ján Jakubík (2003)

Czechoslovak Mathematical Journal

In this paper we deal with the of an M V -algebra 𝒜 , where α and β are nonzero cardinals. It is proved that if 𝒜 is singular and ( α , 2 ) -distributive, then it is . We show that if 𝒜 is complete then it can be represented as a direct product of M V -algebras which are homogeneous with respect to higher degrees of distributivity.

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