Corpus ID: 237503288

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

@inproceedings{Mandal2021ANO,
  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},
  year={2021}
}
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 . 

References

SHOWING 1-9 OF 9 REFERENCES
Remarks on the rings of functions which have a finite numb er of di scontinuities
Let X be an arbitrary topological space. F (X) denotes the set of all real-valued functions on X and C(X)F denotes the set of all f ∈ F (X) such that f is discontinuous at most on a finite set. It isExpand
The Zero-Divisor Graph of a Commutative Ring☆
For each commutative ring R we associate a (simple) graph Γ(R). We investigate the interplay between the ring-theoretic properties of R and the graph-theoretic properties of Γ(R).
Ideals in B1(X) and residue class rings of B1(X) modulo an ideal
<p>This paper explores the duality between ideals of the ring B<sub>1</sub>(X) of all real valued Baire one functions on a topological space X and typical families of zero sets, calledExpand
Zero-divisor graph of C(X)
SummaryIn this article the zero-divisor graph Γ(C(X)) of the ring C(X) is studied. We associate the ring properties of C(X), the graph properties of Γ(C(X)) and the topological properties of X.Expand
On rings of Baire one functions
<p>This paper introduces the ring of all real valued Baire one functions, denoted by B<sub>1</sub>(X) and also the ring of all real valued bounded Baire one functions, denoted byExpand
An algebraic characterization of Blumberg spaces
Click on the link to view the abstract. Keywords: Without isolated point; almost discrete space; irresolvable space; openhereditarily irresolvable space; semiprime ring; Blumberg space QuaestionesExpand
On the ring of functions which are discontinuous on a finite set
  • Houston J. Math. 44 (2)
  • 2018
Jerison, Rings of Continuous Functions, Springer, London
  • 1976