On rings of Baire one functions

Authors

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

DOI:

https://doi.org/10.4995/agt.2019.10776

Keywords:

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

Abstract

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

References

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Published

2019-04-01

How to Cite

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

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Articles