Proximal Lusternik-Schnirelmann, Császár and Bornology Categories

James F. Peters; Tane Vergili; Ebubekir İnan

doi:10.54974/fcmathsci.1703891

Proximal Lusternik-Schnirelmann, Császár and Bornology Categories

Abstract

This paper introduces new forms of proximity space categories, namely, proxLS and dproxLS, spatial and descriptive proximity refinements of the Lusternik-Schnirelmann category LS and desProx, which is a descriptive proximity extension of the Császár Prox category. A main result given here is that a proximity space (X, δ) is proximally contractible if and only if the proximal Lusternik-Schnirelmann category LSδ(X) = 1. Several other results are also given, namely, Prox has all nonempty products and coproducts and ProxBor has all nonempty coproducts.

Keywords

References

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Details

Primary Language

English

Subjects

Topology

Journal Section

Research Article

Authors

James F. Peters
0000-0002-1026-4638
Canada

Tane Vergili ^*
0000-0003-1821-6697
Türkiye

Ebubekir İnan
0000-0002-7269-8941
Türkiye

Publication Date

July 31, 2026

Submission Date

May 21, 2025

Acceptance Date

July 20, 2026

Published in Issue

Year 2026 Volume: 7 Number: 2

DOI

https://doi.org/10.54974/fcmathsci.1703891

IZ

https://izlik.org/JA38KK28SW

Cite

RIS / Bibtex

APA

Peters, J. F., Vergili, T., & İnan, E. (2026). Proximal Lusternik-Schnirelmann, Császár and Bornology Categories. Fundamentals of Contemporary Mathematical Sciences, 7(2), 110-134. https://doi.org/10.54974/fcmathsci.1703891

AMA

1.Peters JF, Vergili T, İnan E. Proximal Lusternik-Schnirelmann, Császár and Bornology Categories. FCMS. 2026;7(2):110-134. doi:10.54974/fcmathsci.1703891

Chicago

Peters, James F., Tane Vergili, and Ebubekir İnan. 2026. “Proximal Lusternik-Schnirelmann, Császár and Bornology Categories”. Fundamentals of Contemporary Mathematical Sciences 7 (2): 110-34. https://doi.org/10.54974/fcmathsci.1703891.

EndNote

Peters JF, Vergili T, İnan E (July 1, 2026) Proximal Lusternik-Schnirelmann, Császár and Bornology Categories. Fundamentals of Contemporary Mathematical Sciences 7 2 110–134.

IEEE

[1]J. F. Peters, T. Vergili, and E. İnan, “Proximal Lusternik-Schnirelmann, Császár and Bornology Categories”, FCMS, vol. 7, no. 2, pp. 110–134, July 2026, doi: 10.54974/fcmathsci.1703891.

ISNAD

Peters, James F. - Vergili, Tane - İnan, Ebubekir. “Proximal Lusternik-Schnirelmann, Császár and Bornology Categories”. Fundamentals of Contemporary Mathematical Sciences 7/2 (July 1, 2026): 110-134. https://doi.org/10.54974/fcmathsci.1703891.

JAMA

1.Peters JF, Vergili T, İnan E. Proximal Lusternik-Schnirelmann, Császár and Bornology Categories. FCMS. 2026;7:110–134.

MLA

Peters, James F., et al. “Proximal Lusternik-Schnirelmann, Császár and Bornology Categories”. Fundamentals of Contemporary Mathematical Sciences, vol. 7, no. 2, July 2026, pp. 110-34, doi:10.54974/fcmathsci.1703891.

Vancouver

1.James F. Peters, Tane Vergili, Ebubekir İnan. Proximal Lusternik-Schnirelmann, Császár and Bornology Categories. FCMS. 2026 Jul. 1;7(2):110-34. doi:10.54974/fcmathsci.1703891