Spaces of lower semicontinuous set-valued maps II

Mathematica Slovaca

R. McCoy¹ 

关键词: lower semicontinuous set-valued map;    multifunction space;    Vietoris topology;    extension theorem;    factorization theorem;    bimonotone homeomorphism;    ordered homeomorphism;   

DOI  :  10.2478/s12175-010-0031-9

学科分类：数学（综合）

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

【 摘 要 】

This is a continuation of “Spaces of lower semicontinuous setvalued maps I”. Together, these two parts contain two interrelated main theorems. In the previous part I, the Extension Theorem is proved, which says that for binormal spaces X and Y, every bimonotone homeomorphism between C(X) and C(Y) can be extended to an ordered homeomorphism between L −(X) and L −(Y). In this part II, the Factorization Theorem is proved, which says that for binormal spaces X and Y, every ordered homeomorphism between L −(X) and L −(Y) can be characterized by a unique factorization.

【 授权许可】

Unknown