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Locally convex spaces of non-Archimedean valued continuous functions

Locally convex spaces of non-Archimedean valued continuous functions

We study the space C( X, K, < 3 ) ) of all continuous functions from the ultraregular space X into the non-Archimedean valued field K with topology of uniform convergence on a family 9 of subsets of the Z-repletion of X.We characterize the bornological space associated to C(X, K, …