Vol. 29, No. 1, 1969

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The lattice of pretopologies on an arbitrary set S

Allan Matlock Weber Carstens

Vol. 29 (1969), No. 1, 67–71
Abstract

The structure of the lattice of pretopologies on the set S, unlike that of the lattice of topologies on S (a proper sublattice of the former), has not been closely examined. We establish that pretopologies may be identified with products of certain filters in a natural way. From this identification, we are able to determine much of the structure of this lattice.

Mathematical Subject Classification
Primary: 54.10
Secondary: 06.00
Milestones
Received: 31 March 1968
Revised: 17 June 1968
Published: 1 April 1969
Authors
Allan Matlock Weber Carstens