On complementation problem in the lattice of L-topologies

Pinky _, T.P. Johnson
Published 2018-07-02
DOI 10.28919/aia/3720

Abstract

In this paper, we study the lattice structure of the lattice FX of all L-topologies on a given nonempty set X. It is proved that the lattice FX is complemented and dually atomic when X is any nonempty set and membership lattice L is a complete atomic boolean lattice. Further we introduce the concept of limit point in the membership lattice and prove that if membership lattice L has a limit point, then for any nonempty set X, the lattice FX is not complemented.
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How to Cite this Article

Pinky _, T.P. Johnson, On complementation problem in the lattice of L-topologies, Adv. Inequal. Appl., 2018 (2018), Article ID 11. https://doi.org/10.28919/aia/3720

Copyright © 2018 Pinky _, T.P. Johnson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.