Pointwise convergence on the rings of functions which are discontinuous on a set of measure zero

• Mandal, Dhananjoy ^[1] ; Singha, Achintya ^[2] ; Bag, Sagarmoy ^[2]
  1. [1] University of Calcutta

     University of Calcutta

     India

     
  2. [2] Bangabasi Evening College
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 25, Nº. 1, 2024, págs. 253-275
• Idioma: inglés
• DOI: 10.4995/agt.2024.18884
• Enlaces
  • Texto completo
• Resumen

  • Consider the ring  ℳ∘ ( X , μ ) of functions which are discontinuous on a set of measure zero which is introduced and studied extensively in [2]. In this paper, we have introduced a ring  B1 ( X , μ ) of functions which are pointwise limits of sequences of functions in ℳ∘ ( X , μ ) . We have studied various properties of zero sets, B1 ( X , μ ) -separated and B1 ( X , μ ) -embedded subsets of B1 ( X , μ ) and also established an analogous version of Urysohn's extension theorem. We have investigated a connection between ideals of B1 ( X , μ ) and ZB -filters on X. We have studied an analogue of Gelfand-Kolmogoroff theorem in our setting. We have defined real maximal ideals of B1 ( X , μ ) and established the result | ℛ M a x ( ℳ∘ ( X , μ ) ) | = | ℛ M a x ( B1 ( X , μ ) ) | , where ℛ M a x ( ℳ∘ ( X , μ ) ) and ℛ M a x ( B1 ( X , μ ) ) are the sets of all real maximal ideals of ℳ∘ ( X , μ ) and B1 ( X , μ ) respectively.

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