Research Article

On bases of closure operators on complete lattices

Published in: Quaestiones Mathematicae
Volume 46 , issue 4 , 2023 , pages: 781–790

DOI: 10.2989/16073606.2022.2041758

Author(s): Josef Šlapal Brno University of Technology, Institute of Mathematics, Czech Republic

Keywords: Primary: 06A15 , Secondary: 54A05 , Complete lattice , pseudocomplement , closure operator , closed base , open base , neighborhood base

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Abstract

We study closure operators on complete lattices and define for them the concepts of closed and open bases as well as that of a neighborhood base. Some properties of these concepts are studied including relationships between them. In particular, we find suﬃcient conditions under which the properties are analogous to those known for topological spaces.

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