A topological characterization of an almost Boolean algebra
DOI:
https://doi.org/10.17398/2605-5686.39.1.47Keywords:
almost distributive lattice, almost Boolean algebra, maximal element, discrete ADL, discrete topology, Boolean spaceAbstract
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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