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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

Issue:

SSRSMI, Number 1, Volume XXVIII

Section:

Volume 28, Number 1

Abstract:

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

Keywords:

Generalized Topology, Dual Topology, Function Space, Admissibility, Splittingness.

Code [ID]:

SSRSMI201801V28S01A0003 [0004810]

Note:

Full paper:

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