The hull-kernel topology on residuated lattices
Abstract
The notion of hull-kernel topology on a collection of prime filters in a residuated lattice is introduced and investigated. It is observed that any collection of prime filters is a topological space under the hull-kernel and the dual hull-kernel topologies. It is proved that any collection of prime filters is a space if and only if it is an antichain, and it is a Hausdorff space if and only if it satisfies a certain condition. Some characterizations in which maximal filters forms a Hausdorff space are given. At the end, it is focused on the space of minimal prim filters, and it is shown that this space is a totally disconnected Hausdorff space. This paper is closed by a discussion abut the various forms of compactness and connectedness of this space.
Keywords
Cite
@article{arxiv.1812.11510,
title = {The hull-kernel topology on residuated lattices},
author = {Saeed Rasouli and Amin Dehghani},
journal= {arXiv preprint arXiv:1812.11510},
year = {2019}
}