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arXiv · 2109.06414

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

Samir Ch Mandal·Sagarmoy Bag·Dhananjoy Mandal
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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 $C(X)_F$.

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Samir Ch Mandal, Sagarmoy Bag, Dhananjoy Mandal. 2021-09-14. A note on the rings of functions which are discontinuous on some finite sets. https://arxiv.org/abs/2109.06414

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