Expansions of subfields of the real field by a discrete set

Philipp Hieronymi

Displaying similar documents to “Expansions of subfields of the real field by a discrete set”

Definably complete Baire structures

Antongiulio Fornasiero, Tamara Servi (2010)

Fundamenta Mathematicae

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We consider definably complete Baire expansions of ordered fields: every definable subset of the domain of the structure has a supremum and the domain cannot be written as the union of a definable increasing family of nowhere dense sets. Every expansion of the real field is definably complete and Baire, and so is every o-minimal expansion of a field. Moreover, unlike the o-minimal case, the structures considered form an axiomatizable class. In this context we prove a version of the Kuratowski-Ulam...

Besicovitch via Baire

T. W. Körner (2003)

Studia Mathematica

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We construct various Besicovitch sets using Baire category arguments.

Iterated Cesàro averages, frequencies of digits, and Baire category

J. Hyde, V. Laschos, L. Olsen, I. Petrykiewicz, A. Shaw (2010)

Acta Arithmetica

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On Riemann's theorem about conditionally convergent series

I. Hozo, H. I. Miller (1986)

Matematički Vesnik

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Baire outer kernels of sets.

Miller, Harry I. (1981)

Publications de l'Institut Mathématique. Nouvelle Série

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Preimages of Baire spaces

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

Mathematica Bohemica

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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.

An analogue of a result of Carathéodory

Harry I. Miller (1981)

Časopis pro pěstování matematiky

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An incompatibility theorem

Harry I. Miller (1984)

Colloquium Mathematicae

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Remarks concerning the invariance of Baire spaces under mappings

Zdeněk Frolík (1961)

Czechoslovak Mathematical Journal

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Baire spaces

R. C. Haworth, R. A McCoy

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CONTENTSIntroduction............................................................................................................ 5I. Basic properties of Baire spaces................................................................... 61. Nowhere dense sets............................................................................................... 62. First and second category sets............................................................................. 83. Baire spaces................................................................................................................