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Advances in Inequalities and Applications ISSN 2050-7461

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Adv. Inequal. Appl. 2018 (2018), Article ID 11

On complementation problem in the lattice of L-topologies

Pinky _, T.P. Johnson

PDF (238.2 KB) https://doi.org/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.

Published
2 July 2018
Volume
2018 (2018)
License
CC BY 3.0

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.

Cite this article

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

BibTeX
@article{_2018,
  author  = {_, Pinky and Johnson, T.P.},
  title   = {On complementation problem in the lattice of L-topologies},
  journal = {Adv. Inequal. Appl.},
  volume  = {2018},
  year    = {2018},
  pages   = {11},
  doi     = {10.28919/aia/3720}
}