Year

1979

Degree Name

Doctor of Philosophy

Department

Department of Mathematics

Abstract

This thesis is concerned with defining a topology-like structure on A-semi-lattices and examining the properties of the associated continuous functions. A general pre-neighbourhood structure, which satisfies the poset analogues of the neighbourhood systems of points in a topological space, is introduced on an A-semi-lattice, and is used to define open elements. However, without the complete atomic Boolean structure of P(X), the supremum of pre-neighbourhood open elements need not be open. Neighbourhood structures are introduced on arbitrary lattices to remove this deficiency.

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