A topological characterization of an almost Boolean algebra
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https://doi.org/10.17398/2605-5686.39.1.47Palabras clave:
almost distributive lattice, almost Boolean algebra, maximal element, discrete ADL, discrete topology, Boolean spaceResumen
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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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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Derechos de autor 2024 The authors
Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial 4.0.
