Pre-neighbourhood A-semi-lattices, neighbourhood lattices, and their associated continuous functions
Year
1979
Degree Name
Doctor of Philosophy
Department
Department of Mathematics
Recommended Citation
Prokop, Frank P., Pre-neighbourhood A-semi-lattices, neighbourhood lattices, and their associated continuous functions, Doctor of Philosophy thesis, Department of Mathematics, University of Wollongong, 1979. https://ro.uow.edu.au/theses/1559
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.
Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong.