A note on the rings of functions which are discontinuous on some finite sets

Samir Ch Mandal; Sagarmoy Bag; Dhananjoy Mandal

A note on the rings of functions which are discontinuous on some finite sets

General Topology 2021-09-15 v1

Authors: Samir Ch Mandal , Sagarmoy Bag , Dhananjoy Mandal

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 $X$ . 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 $C(X)_F$ .

Keywords

rings of functions discontinuous functions finite sets uniform limit zero divisor graph non-isolated points topology

Cite

@article{arxiv.2109.06414,
  title  = {A note on the rings of functions which are discontinuous on some finite sets},
  author = {Samir Ch Mandal and Sagarmoy Bag and Dhananjoy Mandal},
  journal= {arXiv preprint arXiv:2109.06414},
  year   = {2021}
}

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