A topological characterization of an almost Boolean algebra

Authors

  • K. Ramanuja Rao Department of Mathematics, Fiji National University Lautoka, P.O. Box 5529, Fiji
  • K. Rama Prasad Department of Engineering Mathematics, Andhra University Visakhapatnam - 530003, A.P., India
  • G. Vara Lakshmi Department of Engineering Mathematics, Andhra University Visakhapatnam - 530003, A.P., India
  • Ch. Santhi Sundar Raj Department of Engineering Mathematics, Andhra University Visakhapatnam - 530003, A.P., India

DOI:

https://doi.org/10.17398/2605-5686.39.1.47

Keywords:

almost distributive lattice, almost Boolean algebra, maximal element, discrete ADL, discrete topology, Boolean space

Abstract

For any Boolean space X and a discrete almost distributive lattice D, it is proved that the set C(X, D) of all continuous mappings of X into D, when D is equipped with the discrete topology, is an almost Boolean algebra under pointwise operations. Conversely, it is proved that any almost Boolean algebra is a homomorphic image of C(X,D) for a suitable Boolean space X and a discrete almost distributive lattice D.

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References

Ch. Santhi Sundar Raj, K. Rama Prasad, M. Santhi, R. Vasu Babu, The C(X, D), a characterization of a Stone almost distributive lattice, Asian-Eur. J. Math. 8 (3) (2015), 1550055, 7 pp.

R.C. Mani, K. Krishna Rao, K. Rama Prasad, Ch. Santhi Sundar Raj, Sheaf representation of almost Boolean algebras, Int. J. Math. Comput. Sci. (communicated) (2022).

U.M. Swamy, Ch. Santhi Sundar Raj, R. Chudamani, On almost Boolean algebras and rings, International Journal of Mathematical Archive 7 (12) (2016), 1 – 7.

U.M. Swamy, Ch. Santhi Sundar Raj, R. Chudamani, Annihilators and maximisors in ADL’s, International Journal of Computer and Mathematical Research 5 (1) (2017), 1770 – 1782.

U.M. Swamy, G.C. Rao, Almost distributive lattices, J. Austral. Math. Soc. Ser. A 31 (1981), 77 – 91.

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Published

2024-05-31

Issue

Section

Functional Analysis and Operator Theory

How to Cite

A topological characterization of an almost Boolean algebra. (2024). Extracta Mathematicae, 39(1), 47-55. https://doi.org/10.17398/2605-5686.39.1.47