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Completion of Countably Seminormed Spaces
Authors:M Merkle
Institution:(1) Department of Applied Mathematics, Faculty of Electrical Engineering, P.O. Box 35-54, 11120 Belgrade, Yugoslavia
Abstract:Let E be a vector space with a topology generated by countably many increasing seminorms p1 lE p2 lE...and let Emacrp i be the completion of E/ker (pi) with respect to pi. If pi are norms compatible in a certain sense, it is known that E is a complete space if and only if E=capi=1 infinEmacrp i . In this paper we give a similar characterization of complete spaces in a general case when pi are seminorms, without any additional assumptions. Our characterization coincides with the known one if pi are compatible norms.
Keywords:
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