Mathematica Slovaca | |
Spaces of lower semicontinuous set-valued maps I | |
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/s12175-010-0030-x | |
学科分类:数学(综合) | |
来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute | |
【 摘 要 】
We introduce a lower semicontinuous analog, L −(X), of the well-studied space of upper semicontinuous set-valued maps with nonempty compact interval images. Because the elements of L −(X) contain continuous selections, the space C(X) of real-valued continuous functions on X can be used to establish properties of L −(X), such as the two interrelated main theorems. The first of these theorems, the Extension Theorem, is proved in this Part I. The Extension Theorem 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). The second main theorem, the Factorization Theorem, is proved in Part II. The Factorization Theorem 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
【 预 览 】
Files | Size | Format | View |
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RO201912080690812ZK.pdf | 442KB | download |