On rings of real-valued Rcl-supercontinuous functions

Authors

  • Masoumeh Etebar Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran
  • Somayeh Soltanpour Department of Science, Petroleum University of Technology, Ahvaz, Iran

Keywords:

Rcl-supercontinuous function, Prcl-space, almost Prcl-space, rcl-compact space, scl-completely regular space.

Abstract

The notion of Rcl-supercontinuity, a strong variant of continuity, is considered. The ring Rcl(X) of all real valued Rcl-supercontinuous functions on a topological space X is studied.

It is shown that Rcl(X) ∼ =C(Y), where Y is an ultra-Hausdorff rcl-quotient of X and it turns out that whenever X is rcl-compact, then Y is zero-dimensional. The maximal ideals of Rcl(X) are specified. The spaces X are determined for which every maximal ideal in Rcl(X) is fixed. Finally, Prcl-spaces and almost Prcl-spaces are defined and characterized both algebraically and topologically.

 

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Published

2021-11-27

Issue

Vol. 16

Section

Vol. 16, No. 10, (2022)

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