Set-valued generalizations of Baire's category theorem
type: Item
instance of: scholarly article
title: Set-valued generalizations of Baire's category theorem
zbMATH Open document ID: 0843.54032
author: Piotr Urbaniec
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-08-15T00:00:00Z
review text: The classical Mittag-Leffler theorem asserts that if \(\{X_k\}\) is a sequence of complete metric spaces and \(f_k: X_k\to X_{k-1}\) is a continuous function with \(f_k (X_k)\) dense in \(X_{k-1}\), then \(\bigcap^\infty_{k=1} f_1\circ \dots \circ f_k(X_k)\) is dense in \(X_0\). In this well-written article the author extends the Mittag-Leffler theorem to Čech-complete topological spaces and continuous closed-valued multifunctions with dense ranges. The methods of Stone-Čech compactification of the spaces \(X_i\), \(i=1, 2,\dots\) are incorporated. An example showing the necessity of the closedness of the values of multifunctions is provided. A question is asked whether the continuity may be replaced by lower semicontinuity.
Mathematics Subject Classification ID: 54E52
Mathematics Subject Classification ID: 54C60
zbMATH DE Number: 861795
zbMATH Keywords: Čech-completeness
zbMATH Keywords: Mittag-Leffler theorem
zbMATH Keywords: Čech-complete topological spaces
zbMATH Keywords: multifunctions
zbMATH Keywords: lower semicontinuity
reviewed by: Zbigniew Piotrowski
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1387
OpenAlex ID: W1985368923
DOI: 10.1006/JMAA.1995.1387
Recommended article: A generalization of Baire's category theorem
Recommended article: Q4680156
Recommended article: Q4396139
Recommended article: Non-Baire sets in category bases
Recommended article: Q4495407
Recommended article: Baire category and zero sets
Recommended article: An analogue of the Baire category theorem
Recommended article: The Baire Category Property and Some Notions of Compactness
Recommended article: About some categories of \(\Omega\)-valued sets
Recommended article: Q5060247
description: scientific article; zbMATH DE number 861795