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BASIC PROPERTIES OF K-SPACES

Charles、Swartz

1992系统科学与复杂性：英文版Decision Sciences被引 0

摘要

Every complete metric linear space is a K-space.A non-completenormed space can be a K-space.And non-metrizable K-spaces exist.A series ofbasic results on complete metric linear spaces Can be generalized to K-spaces.Forexample,every bounded linear operator from a K-space into a locally convex spaceis sequentially continuous;every bounded semi-norm on a K-space is sequentiallycontinuous and,therefore,piecewise separable;a.C-sequeatial K-space is both bar-relled and bornological;the family of sequentially continuous linear functionals ona K-space is weak sequentially complete.

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