On rings of Baire one functions

Abstract

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