Lattice-valued convergence spaces and regularity
The author continues his previous studies on lattice-valued convergence spaces. The main purpose of this paper is to use some duality conditions in order to characterize regularity of such spaces with the lattice in the form of a complete Heyting algebra. Moreover some separation axioms are introduced and they are used to prove some theorems on the regularity preservation. Yet another result derived in the paper is given by an extension theorem for continuous mappings from a dense subspace to a regular space. The regularity axiom presented in the paper is also characterized in the restricted lattice context of complete Boolean algebras.
scientific article; zbMATH DE number 5599471
scientific article