Topological Spaces of E-Filters on MS-Almost Distributive Lattices

In this paper, we introduce the concept of [Formula: see text]-filters of MS-Almost Distributive Lattices (MS-ADLs) and their important properties are studied. It is proved that the set of all [Formula: see text]-filters of an MS-ADL forms a complete distributive lattice. The concept of [Formula: see text]-filters of an MS-ADL is introduced and a set of equivalent conditions under which every [Formula: see text]-filter is a [Formula: see text]-filter are given. In addition, we characterize [Formula: see text] - filter of an MS-ADL [Formula: see text] in terms of prime filters of [Formula: see text]. The fact that the lattice of all e-filters of an MS-ADL is isomorphic with the lattice of all prime e-filters is proved. Following this, the base for the topology of the space of all prime e-filters of an MS-ADL is identified and an anti-homomorphic map is defined from an MS-ADL [Formula: see text] onto the lattice of all compact open subsets of the space of all prime e-filters of M.