Abstract
In [1] Atherton has asked whether the ideal topology (see [1]) is Hausdorff on every distributive lattice. He also gave some sufficient conditions (Kent's conditions cl and c3 [1]) under which the ideal topology on a complete distributive lattice is Hausdorff. In this paper we determine some more classes of lattices in which the ideal topology is Hausdorff and give examples to show that the classes determined are independent even in a complete distributive lattice. We also show by an example that Atherton's conditions are not necessary even in the case of a complete distributive lattice.
Publisher
Cambridge University Press (CUP)
Cited by
1 articles.
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1. On focal function with respect to the i-open set in i-topological proximity space;INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING ICCMSE 2021;2023