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Points with maximal Birkhoff average oscillation

Jinjun Li, Min Wu (2016)

Czechoslovak Mathematical Journal

Let $f : X \to X$ be a continuous map with the specification property on a compact metric space $X$ . We introduce the notion of the maximal Birkhoff average oscillation, which is the “worst” divergence point for Birkhoff average. By constructing a kind of dynamical Moran subset, we prove that the set of points having maximal Birkhoff average oscillation is residual if it is not empty. As applications, we present the corresponding results for the Birkhoff averages for continuous functions on a repeller and locally...

Porosity and compacta with dense ambiguous loci of metric projections

Jan Kolář (1998)

Acta Universitatis Carolinae. Mathematica et Physica

Préimages d’espaces héréditairement de Baire

Ahmed Bouziad (1997)

Fundamenta Mathematicae

The main result is slightly more general than the following statement: Let f: X → Y be a quasi-perfect mapping, where X is a regular space and Y a Hausdorff totally non-meagre space; if X or Y is χ-scattered, or if Y is a Lasnev space, then X is totally non-meagre. In particular, the product of a compact space X and a Hausdorff regular totally non-meagre space Y which is χ-scattered or a Lasnev space, is totally non-meagre.

Preimages of Baire spaces

Jozef Doboš, Zbigniew Piotrowski, Ivan L. Reilly (1994)

Mathematica Bohemica

A simple machinery is developed for the preservation of Baire spaces under preimages. Subsequently, some properties of maps which preserve nowhere dense sets are given.

Products of Baire spaces revisited

László Zsilinszky (2004)

Fundamenta Mathematicae

Generalizing a theorem of Oxtoby, it is shown that an arbitrary product of Baire spaces which are almost locally universally Kuratowski-Ulam (in particular, have countable-in-itself π-bases) is a Baire space. Also, partially answering a question of Fleissner, it is proved that a countable box product of almost locally universally Kuratowski-Ulam Baire spaces is a Baire space.

Products, the Baire category theorem, and the axiom of dependent choice

Horst Herrlich, Kyriakos Keremedis (1999)

Commentationes Mathematicae Universitatis Carolinae

In ZF (i.e., Zermelo-Fraenkel set theory without the Axiom of Choice) the following statements are shown to be equivalent: (i) The axiom of dependent choice. (ii) Products of compact Hausdorff spaces are Baire. (iii) Products of pseudocompact spaces are Baire. (iv) Products of countably compact, regular spaces are Baire. (v) Products of regular-closed spaces are Baire. (vi) Products of Čech-complete spaces are Baire. (vii) Products of pseudo-complete spaces are Baire.