ON DUAL TOPOLOGIES FOR FUNCTION SPACES OVER C_{\mu, \nu}

Abstract

Dual topologies for function space topologies between generalized topological spaces are defined. The point-open topology, compact-open topology and (μ,ν)-topology on C_{\mu, \nu} (Y,Z) are shown to be family-open. The notions of splittingness and admissibility for such spaces are introduced. It is proved that a topology on C_{\mu, \nu} (Y,Z) is splitting (resp. admissible) if and only if its dual topology is splitting (resp. admissible). Similarly, a topology on OZ (Y) is splitting (resp. admissible) if and only if its dual topology on C_{\mu, \nu} (Y,Z) is so.

Cuvinte cheie