Subcontinuity

Mathematica Slovaca

Ľubica Holá¹  Branislav Novotný¹ 

关键词: subcontinuous;    locally totally bounded;    USCO multifunction;    Vietoris topology;    Hausdorff uniformity;    ÄŒech complete space;   

DOI  :  10.2478/s12175-012-0013-1

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

We give interesting characterizations using subcontinuity. Let X, Y be topological spaces. We study subcontinuity of multifunctions from X to Y and its relations to local compactness, local total boundedness and upper semicontinuity. If Y is regular, then F is subcontinuous iff $$ar F$$ is USCO. A uniform space Y is complete iff for every topological space X and for every net {F a}, F a ⊂ X × Y, of multifunctions subcontinuous at x ∈ X, uniformly convergent to F, F is subcontinuous at x. A Tychonoff space Y is Čech-complete (resp. G m-space) iff for every topological space X and every multifunction F ⊂ X × Y the set of points of subcontinuity of F is a G δ-subset (resp. G m-subset) of X.

【 授权许可】

Unknown