Archive for Mathematical Logic

, Volume 57, Issue 3–4, pp 195–201 | Cite as

Some remarks on Baire’s grand theorem



We provide a game theoretical proof of the fact that if f is a function from a zero-dimensional Polish space to \( \mathbb N^{\mathbb N}\) that has a point of continuity when restricted to any non-empty compact subset, then f is of Baire class 1. We use this property of the restrictions to compact sets to give a generalisation of Baire’s grand theorem for functions of any Baire class.


Baire class \(\xi \) function Wadge game Eraser game Polish zero Dimensional space Compact set 

Mathematics Subject Classification



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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Mathematical Sciences Joseph-Louis LagrangePolitecnico di TorinoTorinoItaly
  2. 2.Département des systèmes d’informationUniversité de LausanneLausanneSwitzerland

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