Vol. 58, No. 1, 1975

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The generalized interval topology on distributive lattices

Robert Horace Redfield

Vol. 58 (1975), No. 1, 219–242

The author has recently introduced the generalized interval topology on a partially ordered set as an alternative to the standard interval topology. In this paper, the structure of generalized segments in lattices is investigated, and sufficient conditions are given for the generalized interval topology on a distributive lattice to be a lattice topology; adding another condition ensures that the topology is Hausdorff. Similar results are obtained for a slight modification of the generalized interval topology, the generalized star-interval topology, and examples are constructed which illustrate less restrictive situations.

Mathematical Subject Classification
Primary: 06A45
Received: 15 October 1973
Published: 1 May 1975
Robert Horace Redfield