TY - JOUR
TI - A topological characterization of an almost Boolean algebra
PY - 2024/05/31
Y2 - 2024/10/15
JF - Extracta Mathematicae
JA - Extr. Math.
VL - 39
IS - 1
SE - Functional Analysis and Operator Theory
DO - 10.17398/2605-5686.39.1.47
UR - https://doi.org/10.17398/2605-5686.39.1.47
SP - 47--55
AB - 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.
ER -