Exploring the Power of R#-Closed Sets in Generalized Topological Spaces

Veeresha A Sajjanara; Raghavendra K; Govardhana Reddy H G; A Mohanapriya; Madhusudhan C K

doi:10.5269/bspm.80398

Veeresha A Sajjanara Presidency University
Raghavendra K S-VYASA Deemed to be University
Govardhana Reddy H G Alliance University
A Mohanapriya S-VYASA Deemed to be University
Madhusudhan C K S-VYASA Deemed to be University

Résumé

R#-closed sets, defined via a novel closure operator in generalized topologi
cal spaces, ensure containment within R-open sets, offering a weaker yet ro
bust alternative to classical closure. This paper establishes R#-regularity, R#
compactness, and proves key structural properties including intersection clo
sure and connectedness. Through rigorous examples and original diagrams, we
demonstrate their utility in topological data analysis, network integrity, and
neural robustness, bridging abstract theory with practical modeling in complex
systems.

Téléchargements

Les données sur le téléchargement ne sont pas encore disponible.

Références

[1] Császár, Á. (2020). Generalized topology and its applications. Acta Math.
Hung., 160(1), 1–15. DOI
[2] Ittanagi, B. M., & Raghavendra, K. (2018). On R#-continuous and R#
irresolute maps in topological spaces. Int. J. Adv. Res., 6(2), 461–470.
7
[3] Ittanagi, B. M., & Raghavendra, K. (2017). On R#-closed sets in topolog
ical spaces. Int. J. Math. Appl., 8(8), 134–141.
[4] Ittanagi, B. M., & Raghavendra, K. (2017). On R#-open sets in topological
spaces. J. Comput. Math. Sci., 8(11), 614–620.
[5] Willard, S. (2021). Generalized topological spaces and their properties.
Topol. Appl., 298, 107–123. DOI
[6] Levine, N. (2021). Generalized closed sets and separation axioms. Topol.
Proc., 57, 123–134.
[7] Roy, B. (2022). Compactness in generalized topological spaces. J. Pure
Appl. Math., 78(3), 245–260.
[8] Devi, R. (2023). Continuity in generalized topologies. Int. J. Math., 29(4),
567–580.
[9] Carlsson, G. (2020). Topological data analysis with persistent homology.
Notices AMS, 67(7), 1023–1035. DOI
[10] Chazal, F. (2022). Topology and machine learning: A survey. J. Mach.
Learn. Res., 23(45), 1–35.
[11] Barabási, A.-L. (2023). Network science and topological methods. Nat. Rev.
Phys., 5(4), 211–225. DOI
[12] Kotiuga, P. R. (2023). Topological methods in cryptography. J. Cryptogr.
Eng., 13(2), 101–115. DOI
[13] Edelsbrunner, H. (2021). Persistent homology in big data analysis. SIAM
J. Appl. Math., 81(3), 987–1005. DOI
[14] LaValle, S. M. (2021). Planning algorithms in topological spaces. IEEE
Robot. Autom. Lett., 6(2), 789–796. DOI
[15] Adams, C. C. (2022). Knot theory in biology. J. Math. Biol., 84(5), 45–60.
DOI
[16] Kitaev, A. (2021). Topological quantum computation. Adv. Theor. Phys.,
12(3), 45–67. DOI
[17] Goodfellow, I. (2023). Topological approaches in deep learning. Neural
Netw., 162, 89–104. DOI
[18] Goodchild, M. F. (2022). Topological methods in geospatial analysis. Int.
J. Geogr. Inf. Sci., 36(7), 1234–1256. DOI
[19] Ghrist, R. (2023). Topological methods in climate modeling. Environ.
Model. Softw., 170, 105–120. DOI