On rings of Baire one functions
Keywords:B1(X), Bâˆ—1(X), zero set of a Baire one function, completely separated by B1(X), B1-embedded, Bâˆ—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 Bâˆ—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 Câˆ—(X) (real valued bounded continuous functions), Bâˆ—1 (X) is a proper subclass of B1(X) in almost every non-trivial situation. Introducing B1-embedding and Bâˆ—1-embedding, several analogous results, especially, an analogue of Urysohn’s extension theorem is established.
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