Abstract
In this paper, we study some properties of the ring \(C(X)_F\) of all real valued functions which are continuous except on some finite subsets of a topological space X. We show that \(C(X)_F\) is closed under uniform limit if and only if the set of all non-isolated points of X is finite. We also initiate and investigate the zero divisor graph of the ring \(C(X)_F\).
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The authors are grateful to the referees for their suggestions towards some improvement of the paper.
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Samir Ch Mandal thanks to UGC, India, for financial support.
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Mandal, S.C., Bag, S. & Mandal, D. Convergence and the zero divisor graph on the ring of functions which are discontinuous on a finite set. Afr. Mat. 34, 43 (2023). https://doi.org/10.1007/s13370-023-01079-z
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DOI: https://doi.org/10.1007/s13370-023-01079-z