TY - JOUR
AU - Deb Ray, A.
AU - Mondal, Atanu
PY - 2019/04/01
Y2 - 2024/08/03
TI - On rings of Baire one functions
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 20
IS - 1
SE -
DO - 10.4995/agt.2019.10776
UR - https://polipapers.upv.es/index.php/AGT/article/view/10776
SP - 237-249
AB - <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>âˆ—</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>âˆ—</sup>(X) (real valued bounded continuous functions), B<sup>âˆ—</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>âˆ—</sup><sub>1</sub>-embedding, several analogous results, especially, an analogue of Urysohn’s extension theorem is established.</p>
ER -