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Quasi-complete ideal lattices

Johnny A. Johnson (1975)

Colloquium Mathematicae

Quasicontinuous spaces

Jing Lu, Bin Zhao, Kaiyun Wang, Dong Sheng Zhao (2022)

Commentationes Mathematicae Universitatis Carolinae

We lift the notion of quasicontinuous posets to the topology context, called quasicontinuous spaces, and further study such spaces. The main results are: (1) A $T_{0}$ space $(X, τ)$ is a quasicontinuous space if and only if $S I (X)$ is locally hypercompact if and only if $(τ_{S I}, \subseteq)$ is a hypercontinuous lattice; (2) a $T_{0}$ space $X$ is an $S I$ -continuous space if and only if $X$ is a meet continuous and quasicontinuous space; (3) if a $C$ -space $X$ is a well-filtered poset under its specialization order, then $X$ is a quasicontinuous space...

Quasi-minimal posets and lattices.

J.L. Hickman (1977)

Journal für die reine und angewandte Mathematik

Quasiorder on Systems of Directed Sets

Ján Jakubík (1974)

Matematický časopis

Quasi-orders of algebras

Jiří Rachůnek (1979)

Časopis pro pěstování matematiky

Quotient structures in lattice effect algebras

Amir Hossein Sharafi, Rajb Ali Borzooei (2019)

Kybernetika

In this paper, we define some types of filters in lattice effect algebras, investigate some relations between them and introduce some new examples of lattice effect algebras. Then by using the strong filter, we find a CI-lattice congruence on lattice effect algebras, such that the induced quotient structure of it is a lattice effect algebra, too. Finally, under some suitable conditions, we get a quotient MV-effect algebra and a quotient orthomodular lattice, by this congruence relation.