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Completely prime <i>L</i>-filters, irreducible <i>L</i>-filters and sobriety


Gunther Jäger
Wei Yao

Abstract

In this paper, for a frame L, we characterize modified sobriety in stratified L-topological spaces and strong L-topological spaces internally using certain classes of stratied L-filters. While the first characterization using completely prime L-filters is trivial and applies to all stratied L-topological spaces, the other one using irreducible L-filters generalizes an approach of R.E. Hoffmann to the lattice-valued case but is restricted to either the case that the lattice is a complete Boolean algebra or to the case of completely distributive lattices and strong L-topological spaces.

Keywords: Lattice-valued filter, lattice-valued topology, sobriety


Journal Identifiers


eISSN: 1727-933X
print ISSN: 1607-3606