Glasnik Matematicki, Vol. 35, No.2 (2000), 283-305.
ON THE STRICT TOPOLOGY IN NON-ARCHIMEDEAN
SPACES OF CONTINUOUS FUNCTIONS
A. K. Katsaras
Department of Mathematics, University of Ioannina, P.O. Box 1186,
451 10 Ioannina, Greece
Abstract. The strict topology, on the space
C(X,E) of all continuous functions on a
toplogical space X with values in a non-Archimedean
locally convex space E, is introduced and several of its
properties are investigated. The dual spaces of
C(X,E), under the strict topology and under the
bounding convergence topology, turn out to be certain spaces of
1991 Mathematics Subject Classification.
Key words and phrases. Nachbin families, weighted spaces, strict topology, non-Archimedean seminorms, bounding sets.
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