Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 18, No. 2, pp. 67-70 (2002)

A Short Remark on Kolmogoroff Normability Theorem

A. Caruso

Universitá di Catania

Abstract: Kolmogoroff normability theorem turns to be a characterization for the complete normability of a topological vector space by replacing the convexity hypothesis with the $\sigma$-convexity one. In particular, the well known theorem that characterizes completeness of a normed vector spaces by means of absolutely convergent series, is obtained as an easy consequence of the Theorem below.

Keywords: Topological Vector Spaces, Normability Criteria, Completeness

Classification (MSC2000): 46A03

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