A Comprehensive Study on SuperHyper Filters and Ultrafilters

Suman Patra; Ajoy Kanti Das; Takaaki Fujita

doi:10.47000/tjmcs.1669097

A Comprehensive Study on SuperHyper Filters and Ultrafilters

Abstract

This paper presents a comprehensive study on superHyper filters and ultrafilters, fundamental concepts in topology and mathematical logic with applications in various fields such as lattice theory and set theory. SuperHyper Filters represent a novel extension of traditional filter theory into the domain of SuperHyper Structures, using higher-order power sets and specialized operators. In this study, we explore the fundamental properties of superHyper filters, their relation to ultrafilters, and their role in extending classical filter theory. Several new characterizations and structural insights are provided, demonstrating how superHyper filters refine existing notions in mathematical analysis. We also look at their uses in functional analysis and abstract algebra, demonstrating their applicability in both theoretical and practical settings. Our findings contribute to a deeper understanding of filter structures and open new avenues for research in generalized topology and beyond.

Keywords

References

Adams, R., Garcia, M., Practical applications of filters in computer science, Computer Mathematics, 35(2015), 901–923.
Anderson, J., White, E., Closure properties of filters under specific operators, Mathematical Models, 28(2013), 401–419.
Booth, D., Ultrafilters on a countable set, Annals of Mathematical Logic, 2(1)(1970), 1–24.
Brown, A., Mathematical analysis using filters, Applied Mathematical Methods, 8(2012), 89–105.
Brown, A., Lee, M.,Filters in mathematical structures, Mathematical Reviews, 18(2018), 301–315.
Cancino-Manr´ıquez, J.,I-Ultrafilters in the rational perfect set model, Journal of Symbolic Logic, 89(1)(2024), 175–194.
Clark, S., Fr´echet filters and their properties, Mathematical Foundations, 12(2016), 601–619.
Das, A.K., Patra, S., Fujita, T., Das, S., Advanced structures in SuperHyper algebra: monoids and ideals, Boletim da Sociedade Paranaense de Matem´atica (3rd Series), 43(2025), 1–17.

Details

Primary Language

English

Subjects

Operator Algebras and Functional Analysis, Topology

Journal Section

Research Article

Authors

Suman Patra
0009-0003-9795-7887
India

Ajoy Kanti Das ^*
0000-0002-9326-1677
India

Takaaki Fujita This is me
0000-0002-9009-8325
Japan

Publication Date

June 30, 2026

Submission Date

April 2, 2025

Acceptance Date

October 24, 2025

Published in Issue

Year 2026 Volume: 18 Number: 2

DOI

https://doi.org/10.47000/tjmcs.1669097

IZ

https://izlik.org/JA57BX59AX

Cite

RIS / Bibtex

APA

Patra, S., Das, A. K., & Fujita, T. (2026). A Comprehensive Study on SuperHyper Filters and Ultrafilters. Turkish Journal of Mathematics and Computer Science, 18(2), 567-575. https://doi.org/10.47000/tjmcs.1669097

AMA

1.Patra S, Das AK, Fujita T. A Comprehensive Study on SuperHyper Filters and Ultrafilters. TJMCS. 2026;18(2):567-575. doi:10.47000/tjmcs.1669097

Chicago

Patra, Suman, Ajoy Kanti Das, and Takaaki Fujita. 2026. “A Comprehensive Study on SuperHyper Filters and Ultrafilters”. Turkish Journal of Mathematics and Computer Science 18 (2): 567-75. https://doi.org/10.47000/tjmcs.1669097.

EndNote

Patra S, Das AK, Fujita T (June 1, 2026) A Comprehensive Study on SuperHyper Filters and Ultrafilters. Turkish Journal of Mathematics and Computer Science 18 2 567–575.

IEEE

[1]S. Patra, A. K. Das, and T. Fujita, “A Comprehensive Study on SuperHyper Filters and Ultrafilters”, TJMCS, vol. 18, no. 2, pp. 567–575, June 2026, doi: 10.47000/tjmcs.1669097.

ISNAD

Patra, Suman - Das, Ajoy Kanti - Fujita, Takaaki. “A Comprehensive Study on SuperHyper Filters and Ultrafilters”. Turkish Journal of Mathematics and Computer Science 18/2 (June 1, 2026): 567-575. https://doi.org/10.47000/tjmcs.1669097.

JAMA

1.Patra S, Das AK, Fujita T. A Comprehensive Study on SuperHyper Filters and Ultrafilters. TJMCS. 2026;18:567–575.

MLA

Patra, Suman, et al. “A Comprehensive Study on SuperHyper Filters and Ultrafilters”. Turkish Journal of Mathematics and Computer Science, vol. 18, no. 2, June 2026, pp. 567-75, doi:10.47000/tjmcs.1669097.

Vancouver

1.Suman Patra, Ajoy Kanti Das, Takaaki Fujita. A Comprehensive Study on SuperHyper Filters and Ultrafilters. TJMCS. 2026 Jun. 1;18(2):567-75. doi:10.47000/tjmcs.1669097