Fisher‘s diagonal condition for lattice-valued convergence spaces

Abstract

We study a generalization of a diagonal condition which classically ensures that a convergence space is topological. We show that only under an additional condition, which classically is always true, the validity of this diagonal condition implies that a Heyting algebra-valued convergence space is L-topological.

Keywords: L-fuzzy convergence, L-topology, L-filter, L-diagonal filter, L-convergence space, pretopological space, diagonal condition

Quaestiones Mathematicae 31(2008), 11–25