The Space of Fuzzy Minimal Prime Filters In an Almost Distributive Lattice

Abstract

In this paper, we establish and describe the notions of fuzzy minimal prime filters of an Almost Distributive Lattice (ADL). We prove that a fuzzy filter is the point wise infimum of all minimal prime fuzzy filters (all fuzzy minimal prime filters) of an ADL. Mainly, we introduce the topological space on the set of all fuzzy minimal prime filters of an ADL (denoted by M(R)). For an ADL R, we prove that an open set M(R) is a base for the topology and it constitutes a base for the subspace topology on a closed set N and they are the only compact open sets.

Keywords

• Almost distributive lattice (ADL)
• fuzzy filter
• prime fuzzy filter
• minimal prime fuzzy filter
• fuzzy prime filter and fuzzy minimal prime filter

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