Format of Original
American Mathematical Society
Proceedings of the American Mathematical Society
Original Item ID
doi: 10.1090/S0002-9939-1976-0405332-5; Shelves: QA1 .A5215 Storage S
Let X be a space and let H(X) denote its hyperspace (= all nonempty closed subsets of X topologized via the Vietoris topology). Then X is Boolean (= totally disconnected compact Hausdorff) iff is Boolean; and if B denotes the characteristic algebra of clopen sets in X then the corresponding algebra for H(X) is the free algebra generated by B modulo the ideal which "remembers" the upper semilattice structure of B.
Bankston, Paul, "Clopen Sets in Hyperspace" (1976). Mathematics, Statistics and Computer Science Faculty Research and Publications. 147.