Vol. 109, No. 2, 1983

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Locally convex spaces of non-Archimedean valued continuous functions

Willy Govaerts

Vol. 109 (1983), No. 2, 399–410
Abstract

We study the space C(X,K,𝒫) of all continuous functions from the ultraregular space X into the non-Archimedean valued field K with topology of uniform convergence on a family 𝒫 of subsets of the Z-repletion of X. We characterize the bornological space associated to C(X,K,𝒫), semi-bornological spaces C(X,K,𝒫), reflexivity and semi-reflexivity both for spherically complete and non-spherically complete K.

Mathematical Subject Classification 2000
Primary: 46P05, 46P05
Secondary: 46E10
Milestones
Received: 8 October 1981
Revised: 15 October 1982
Published: 1 December 1983
Authors
Willy Govaerts