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

ANKIT GUPTA ^{1}, RATNA DEV SARMA ^{2} 1. Department of Mathematics, University of Delhi, Delhi 110007, INDIA.
e-mail : ankitsince1988@yahoo.co.in
2. Department of Mathematics, Rajdhani College (University of Delhi), Delhi 110015, INDIA.
e-mail : ratna_sarma@yahoo.com

Dual topologies for function space topologies between generalized topological spaces are defined. The point-open topology, compact-open topology and (ÎŒ,Îœ)-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.