Vol. 23, No. 3, 1967

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Superatomic Boolean algebras

George Wesley Day

Vol. 23 (1967), No. 3, 479–489

A Boolean algebra B can be imbedded in a complete Boolean algebra C in such a way that all homomorphisms of B into complete Boolean algebras can be extended to complete homomorphisms on C if and only if B is superatomic, that is, every homomorphic image of B is atomic. This paper is a study of the structure of superatomic Boolean algebras, through the development of techniques of construction and classification, and through the representation of these algebras as compact Hausdorff clairsemé spaces.

Mathematical Subject Classification
Primary: 06.60
Received: 27 January 1967
Published: 1 December 1967
George Wesley Day