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

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Amar Kumar Banerjee, Indrajit Debnath

General Topology · Submitted 17 Oct 2023

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Also we have formulated a weaker condition for the sequences so that the classical density topology coincides with $\mathcal{I}_{(s)}$-density topology.

how it is stated · asserted 1.00 read the record →

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arXiv ID2310.11090 (version 1)
Pith IDBLSEOLF5, Pith's permanent record of this paper and its review
CitationAmar Kumar Banerjee, Indrajit Debnath. "On a generalized density point defined by families of sequences involving ideals." arXiv:2310.11090 (2023). https://pith.science/paper/BLSEOLF5
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,018 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.17 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.67 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 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. contribution 1.00 0.94 0.17 asserted 1.00
s1 We have studied the corresponding topology in the space of reals and have investigated several properties of this topology. contribution 1.00 0.95 0.11 asserted 1.00
s2 Also we have formulated a weaker condition for the sequences so that the classical density topology coincides with $\mathcal{I}_{(s)}$-density topology. result 0.59 0.94 0.36 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.84 · evidence from proof or derivation 1.00.

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sources read
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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

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.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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