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R-F-spaces and subrings of C(X)

  • Rezaei Aliabad, Ali [1] ; Joula, Maryam [1] ; Paimann, Monireh [1] ; Parsinia, Mehdi [2]
    1. [1] Shahid Chamran University of Ahvaz

      Shahid Chamran University of Ahvaz

      Irán

    2. [2] University of Cologne

      University of Cologne

      Kreisfreie Stadt Köln, Alemania

  • Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 27, Nº. 2, 2026
  • Idioma: inglés
  • DOI: 10.4995/agt.24521
  • Enlaces
  • Resumen

    • A topological space X is said to be an F-space if the ring C(X), the algebra of all real-valued continuous functions on X, is a Bézout ring (i.e., every finitely generated ideal in C(X) is principal). This is a classical concept in the context of C(X), and various generalizations of this notion have been introduced. In this paper, associated with a subring R of C(X), we introduce and study the notion of R-F-spaces as a new extension of F-spaces. We investigate a number of characterizations of R-F-spaces by extending some of the well-known facts in the literature of C(X) to lattice-ordered subrings, and some other classes of subrings of C(X), namely, SZ -subrings and invertible subrings. It turns out that this new generalization includes previous ones as a special case, thereby establishing strong connections with the existing results in this context.

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