P-adic Measures and P-adic Spaces of Continuous Functions


For X a Hausdorff zero-dimensional topological space and E a Hausdorff  non-Archimedean locally convex space, let C(X,E) (resp. C_{b}(X,E)) be  the space of all continuous (resp.  bounded continuous ) E-valued functions  on X. Some of the properties of the spaces C(X,E),\ \ C_{b}(X,E),  equipped with certain locally convex topologies, are studied. Also, some  complete spaces of measures, on the algebra of all clopen subsets of X, are  investigated.

DOI Code: 10.1285/i15900932v30n1p61

Non-Archimedean fields; zero-dimensional spaces; Banaschewski compactification; locally convex spaces

Classification: 46S10; 46G10

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