arXiv subjects

Indrajit Debnath

Publications and source records attributed to Indrajit Debnath.

4 recordsLinked to original sources

arXiv2024

On sparse set topology using ideals in the space of reals

In this paper we have introduced the notion of $\mathcal{I}$-sparse set in the space of reals and explored some properties of the family of $\mathcal{I}$-sparse sets. Thereafter we have induced a topology namely $\mathcal{I}$-sparse set topology in the space of reals and it has been observed that this topology is finer than $\mathcal{I}-$density topology introduced by Banerjee and Debnath in \cite{banerjee 4}. We further studied some salient properties of this topology.

math.GN↗

arXiv2023

On a generalized density point defined by families of sequences involving ideals

In this paper we have introduced the notion of $\mathcal{I}_{(s)}$-density point corresponding to the family of unbounded and $\mathcal{I}$-monotonic increasing positive real sequences, where $\mathcal{I}$ is the ideal of subsets of the set of natural numbers. We have studied the corresponding topology in the space of reals and have investigated several properties of this topology. Also we have formulated a weaker condition for the sequences so that the classical density topology coincides with $\mathcal{I}_{(s)}$-density topology.

math.GN↗

arXiv2023

On some topology generated by $\mathcal{I}$-density function

In this paper we have studied on $\mathcal{I}$-density function using the notion of $\mathcal{I}$-density, introduced by Banerjee and Debnath \cite{banerjee 4} where $\mathcal{I}$ is an ideal of subsets of the set of natural numbers. We have explored certain properties of $\mathcal{I}$-density function and induced a topology using this function in the space of reals namely $\mathcal{I}$-density topology and we have given a characterization of the Lebesgue measurable subsets of reals in terms of Borel sets in $\mathcal{I}$-density topology.

math.GN↗

arXiv2022

On density topology using ideals in the space of reals

In this paper we have introduced the notion of $\mathcal{I}$-density topology in the space of reals introducing the notions of upper $\mathcal{I}$-density and lower $\mathcal{I}$-density where $\mathcal{I}$ is an ideal of subsets of the set of natural numbers. We have further studied certain separation axioms of this topology.

math.GN↗