On rings of Baire one functions

• Autores: Atasi Debray, Atanu Mondal
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 20, Nº. 1, 2019, págs. 237-249
• Idioma: inglés
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• Resumen

  • This paper introduces the ring of all real valued Baire one functions, denoted by $B_1(X)$ and also the ring of all real valued bounded Baire one functions, denoted by $B_1^*(X)$. Though the resemblance between $C(X)$ and$B_1(X)$ is the focal theme of this paper, it is observed that unlike $C(X)$ and$C_1^*(X)$ (real valued bounded continuous functions), $B_1^*(X)$ is a proper subclass of $B_1(X)$ in almost every non-trivial situation. Introducing $B_1$-embedding and $B_1^*$-embedding, several analogous results, especially, an analogue of Urysohn's extension theorem is established.