On rings of Baire one functions


  • A. Deb Ray University of Calcutta
  • Atanu Mondal University of Calcutta




B1(X), B∗1(X), zero set of a Baire one function, completely separated by B1(X), B1-embedded, B∗1-embedded


This paper introduces the ring of all real valued Baire one functions, denoted by B1(X) and also the ring of all real valued bounded Baire one functions, denoted by B∗1(X). Though the resemblance between C(X) and B1(X) is the focal theme of this paper, it is observed that unlike C(X) and C∗(X) (real valued bounded continuous functions), B∗1 (X) is a proper subclass of B1(X) in almost every non-trivial situation. Introducing B1-embedding and B∗1-embedding, several analogous results, especially, an analogue of Urysohn’s extension theorem is established.


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Author Biographies

A. Deb Ray, University of Calcutta

Department of Pure Mathematics, Assistant Professor.

Atanu Mondal, University of Calcutta

Department of Pure Mathematics,Research Scholar


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How to Cite

A. Deb Ray and A. Mondal, “On rings of Baire one functions”, Appl. Gen. Topol., vol. 20, no. 1, pp. 237–249, Apr. 2019.