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

被引：7

作者：

Hola, L'. ^{[1
]}

Jain, Tanvi ^{[2
]}

McCoy, R. A. ^{[3
]}

机构：

[1] Slovak Acad Sci, Inst Math, Bratislava 81473, Slovakia

[2] Indian Inst Technol, Dept Math, New Delhi 110016, India

[3] Virginia Tech, Dept Math, Blacksburg, VA 24060 USA

来源：

MATHEMATICA SLOVACA | 2008年 / 58卷 / 06期

关键词：

Primary; 54C60; 54B20; 54A25; 54E35; 54D65; cusco maps; multifunction space; Vietoris topology; upper Vietoris topology; lower Vietoris topology; cardinal functions; metrizability; complete metrizability; countability properties;

D O I：

10.2478/s12175-008-0107-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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 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.

引用

页码：763 / 780

页数：18

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