Semi-continuous multifunctions and bases of countable order

被引：3

作者：

Alleche, B ^{[1
]}

Calbrix, J ^{[1
]}

机构：

[1] Univ Rouen, CNRS, UPRESA 60 85, F-76821 Mt St Aignan, France

来源：

TOPOLOGY AND ITS APPLICATIONS | 2000年 / 104卷 / 1-3期

关键词：

lower semi-continuous multifunction; upper semi-continuous multifunction; selection; base of countable order; weak development; completeness;

D O I：

10.1016/S0166-8641(99)00015-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to the problem of selections. An important result in this area is Michael's theorem on double selection for lower semi-continuous closed valued multifunctions. Recently we obtained a generalization of this theorem to a subclass of the so-called generalized metric spaces, namely the class of weakly developable spaces. One of the aims of this paper is to give an extension of our result (hence of Michael's result) to a more general class of spaces, namely the class of spaces with a base of countable order. To do this, we give some results on spaces with a base of countable order which extend those of Wicke and Worrell Jr. Some applications are given. In particular we obtain a criterion of metrizability. (C) 2000 Published by Elsevier Science B.V. All rights reserved.

引用

页码：3 / 12

页数：10