Lattice-valued convergence spaces and regularity

: We define a regularity axiom for lattice-valued convergence spaces where the lattice is a complete Heyting algebra. To this end, we generalize the characterization of regularity by a "dual form" of a diagonal condition. We show that our axiom ensures that a regular T1-space is separated and that regularity is preserved under initial constructions. Further we present an extension theorem for a continuous mapping from a subspace to a regular space. A characterization in the restricted case that the lattice is a complete Boolean algebra in terms of the closure of an L-filter is given.

• Type: Journal
• Year: 2008
• Where: FSS
• Authors: Gunther Jäger
• Keywords: Complete Heyting Algebra, FSS 2008, Lattice-valued Convergence, Regularity Axiom