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Title: Dense Continuity and Selections of Set-Valued Mappings
Authors: Kenderov, Petar
Moors, Warren
Revalski, Julian
Keywords: Set-Valued Mappings
Selections, Semi-Continuity
Baire Category
Issue Date: 1998
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 24, No 1, (1998), 49p-72p
Abstract: A theorem proved by Fort in 1951 says that an upper or lower semi-continuous set-valued mapping from a Baire space A into non-empty compact subsets of a metric space is both lower and upper semi-continuous at the points of a dense Gδ -subset of A. In this paper we show that the conclusion of Fort’s theorem holds under the weaker hypothesis of either upper or lower quasi-continuity. The existence of densely defined continuous selections for lower quasi-continuous mappings is also proved.
Description: ∗ The first and third author were partially supported by National Fund for Scientific Research at the Bulgarian Ministry of Science and Education under grant MM-701/97.
ISSN: 1310-6600
Appears in Collections:Volume 24 Number 1

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