Applications of the Baire category theorem
type: Item
instance of: scholarly article
title: Applications of the Baire category theorem
zbMATH Open document ID: 0943.26013
author: Sara Hawtrey Jones
published in: Real Analysis Exchange
publication date: 2000-05-21T00:00:00Z
review text: This survey presents many apparently different results where the Baire Category Theorem was applied. Starting with the classical results in real functions theory like the functions without finite derivative at any point, typical \(C^\infty \) non analytic functions, the paper proceeds to the level sets and intersection patterns of typical continuous functions. A big part is devoted to the \(\omega\)-limit sets and attractors of a typical continuous function. Also, the questions how the typical compact continua in Euclidean space look like are showed to be answered by category argument.
Mathematics Subject Classification ID: 26A18
Mathematics Subject Classification ID: 26A15
Mathematics Subject Classification ID: 26A27
zbMATH DE Number: 1449431
zbMATH Keywords: Baire category theorem
zbMATH Keywords: typical continuous functions
zbMATH Keywords: \(\omega \)-limit sets
zbMATH Keywords: level sets
zbMATH Keywords: intersection patterns
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1449431