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COMPACT SPACES OF THE FIRST BAIRE CLASS THAT HAVE OPEN FINITE DEGREE

Part of: Fairly general properties Extremal combinatorics Graph theory Set theory Connections with other structures, applications Real functions

Published online by Cambridge University Press:  21 November 2016

Antonio Avilés  and
Stevo Todorcevic
Antonio Avilés
Affiliation:
Universidad de Murcia, Departamento de Matemáticas, Campus de Espinardo 30100 Murcia, Spain ([email protected])
Stevo Todorcevic
Affiliation:
Institut de Mathématiques de Jussieu, CNRS UMR 7586, Case 247, 4 place Jussieu, 75252 Paris Cedex, France Department of Mathematics, University of Toronto, Toronto, Canada  M5S 3G3 ([email protected]; [email protected])
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Abstract

We introduce the open degree of a compact space, and we show that for every natural number $n$, the separable Rosenthal compact spaces of degree $n$ have a finite basis.

Keywords

Rosenthal compactfirst Baire class functionmultidimensionalsplit intervalAlexandroff duplicate

MSC classification

Primary: 26A21: Classification of real functions; Baire classification of sets and functions 03E15: Descriptive set theory 05C05: Trees 05D10: Ramsey theory 54D30: Compactness 54D55: Sequential spaces 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 17 , Issue 5 , November 2018 , pp. 1173 - 1196
Copyright
© Cambridge University Press 2016 

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Footnotes

First author supported by MINECO and FEDER (MTM2014-54182-P) and by Fundación Séneca - Región de Murcia (19275/PI/14). Second author partially supported by grants from NSERC and CNRS.

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