On rings of Baire one functions

A. Deb Ray; Atanu Mondal

doi:10.4995/agt.2019.10776

Authors

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

DOI:

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

Keywords:

B1(X), Bâˆ—1(X), zero set of a Baire one function, completely separated by B1(X), B1-embedded, Bâˆ—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^âˆ—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^âˆ—(X) (real valued bounded continuous functions), B^âˆ—₁ (X) is a proper subclass of B₁(X) in almost every non-trivial situation. Introducing B₁-embedding and B^âˆ—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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