#### 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

*e-mail:* `akatsar@cc.uoi.gr`

**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
*E*'-valued measures.

**1991 Mathematics Subject Classification.**
46S10.

**Key words and phrases.** Nachbin families, weighted spaces, strict topology, non-Archimedean seminorms, bounding sets.

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