Theorems in functional analysis

Kolmogorov's normability criterion

In mathematics, Kolmogorov's normability criterion is a theorem that provides a necessary and sufficient condition for a topological vector space to be normable; that is, for the existence of a norm on the space that generates the given topology. The normability criterion can be seen as a result in same vein as the Nagata–Smirnov metrization theorem and Bing metrization theorem, which gives a necessary and sufficient condition for a topological space to be metrizable. The result was proved by the Russian mathematician Andrey Nikolayevich Kolmogorov in 1934. (Wikipedia).

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Related pages

Bounded set (topological vector space) | Neighbourhood (mathematics) | Norm (mathematics) | Topological space | Bing metrization theorem | Nagata–Smirnov metrization theorem | Mathematics | Metrizable space | Topology | Theorem | T1 space | Hausdorff space | Convex set | Topological vector space