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

2021/09/14 by Mandal, Samir Ch, Bag, Sagarmoy, Mandal, Dhananjoy
#FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2109.06414

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.

Related

• Rings of functions which are discontinuous on a finite set with countable range
• Zero-divisor graph and comaximal graph of rings of continuous functions with countable range
• Rings of functions whose closure of discontinuity set is in an ideal of closed sets
• The ring of real-valued functions which are continuous on a dense cozero set
• Algebraic properties of the ring C(X)_P