Topological properties of the multifunction space L(X) of cusco maps

Mathematica Slovaca

Ľ. Holá¹  Tanvi Jain¹  R. McCoy¹ 

关键词: cusco maps;    multifunction space;    Vietoris topology;    upper Vietoris topology;    lower Vietoris topology;    cardinal functions;    metrizability;    complete metrizability;    countability properties;   

DOI  :  10.2478/s12175-008-0107-y

学科分类：数学（综合）

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

【 摘 要 】

A set-valued mapping F from a topological space X to a topological space Y is called a cusco map if F is upper semicontinuous and F(x) is a nonempty, compact and connected subset of Y for each x ∈ X. We denote by L(X), the space of all subsets F of X × ℝ such that F is the graph of a cusco map from the space X to the real line ℝ. In this paper, we study topological properties of L(X) endowed with the Vietoris topology.

【 授权许可】

Unknown