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
• DOI: 10.4995/agt.2019.10776
• Enlaces
  • Texto completo
• 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.

• Referencias bibliográficas
  • J. P. Fenecios and E. A. Cabral, On some properties of Baire-1 functions, Int. Journal of Math. Analysis 7, no. 8 (2013), 393-402. https://doi.org/10.12988/ijma.2013.13035
  • I. Gelfand and A. Kolmogoroff, On rings of continuous functions on topological spaces, Dokl. Akad. Nauk SSSR 22 (1939), 11-15.
  • L. Gillman and M. Jerison, Rings of Continuous Functions, New York: Van Nostrand Reinhold Co., 1960. https://doi.org/10.1007/978-1-4615-7819-2
  • E. Hewitt, Rings of real-valued continuous functions, I, Trans. Amer. Math. Soc. 64 (1948), 54-99. https://doi.org/10.1090/S0002-9947-1948-0026239-9
  • P. Y. Lee, W. K. Tang and D. Zhao, An equivalent definition of functions of the first Baire class, Proc. Amer. Math. Soc. 129, no. 8 (2000),...
  • M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), 375-481. https://doi.org/10.1090/S0002-9947-1937-1501905-7
  • L. Vesely, Characterization of Baire-one functions between topological spaces, Acta Universitatis Carolinae Mathematica et Physica 33, no....
  • D. Zhao, Functions whose composition with Baire class one functions are Baire class one, Soochow Journal of Mathematics 33, no. 4 (2007),...