BASIC PROPERTIES OF K-SPACES  

作　　者：CHARLES Swartz 

机构地区：[1]Department of Mathematics,New Mexico State Univercity,Las Cruces,U.S.A.

出　　处：《Systems Science and Mathematical Sciences》1992年第3期233-238,共6页

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.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.

关 键 词：K-SPACE K-convergence K-MATRIX PIECEWISE SEPARABILITY 

分 类 号：N94[自然科学总论—系统科学]