Applications of the Baire category theorem
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.
scientific article; zbMATH DE number 1449431