Vol. 25 No. 2 (2026): Mapana Journal of Sciences
Research Articles

Ggβ*- Compactness in Grill Topological Spaces

Gomathi Rajakumari P.
Department of Mathematics and Research Centre, Sarah Tucker College, Tirunveli - 7 (Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunveli - 12, Tamil Nadu, India)
Jessie Theodore
Department of Mathematics and Research Centre, Sarah Tucker College, Tirunelveli - 7, (Affiliated to Manonmaniam Sundarnar University, Abishekapatti, Tirunveli - 12, Tamil Nadu, India)

Published 2026-07-16

Keywords

  • GgU03B2 - closed set,
  • GgU03B2 - open cover,
  • GgU03B2 - compact,
  • GgU03B2 - continuous function,
  • Grill Topological Spaces

Abstract

In this paper, we have introduced and investigated the characterizations of - compact space in Grill topological spaces. Also compatible- - compact space and countably - - compact space are introduced and some of the equivalent conditions are discussed.

References

  1. Azzam A A, Hussein S S & Saber Osman H, 2020, Compactness of Topological Spaces with Grills, Italian Journal of Pure and Applied Mathematics – N. 44 (198–207).
  2. Choquet G, 1947, Sur les notions de filtre et de Grille, Completes Rendus Acad. Sci. Paris, 224, 171-173.
  3. Gomathi Rajakumari P & Jessie Theodore, 2024, Gg - closure and Gg - interior in Grill Topological Spaces, Nanotechnology Perceptions Vol - 20, No: 8, 544-552
  4. Gomathi Rajakumari P & Jessie Theodore, 2025, Gg - closed sets in Grill Topological Spaces, Indian Journal of Natural Sciences Vol - 15, Issue 88.
  5. Glaisa T Catalan, 2019, “On -open sets and ideals
  6. in Topological Spaces”, European Jouranal of pure
  7. and applied Mathematics, Vol.12, No.3, 893-905.
  8. Karthika A and Arockiarani I, 2013, Generalization of compactness using Grills, International Jounal of Mathematical Archive, 4, 284-288.
  9. Karthika A and Prathiba SR, 2020, -compactness in Grill Topological Spaces, Malaya Journal of Matematik, Vol. No. 2, 1443 – 1446.
  10. Nasef A A and Azzam A A, 2017, On class of function via Grill, Journal of New Theory, 17, 18-25.
  11. Ranchin D V, 1972, Compactness modulo an ideal, Sov. Math. Dokl, 193 – 197.
  12. Roy B & Mukherjee M N, 2007, On a type of compactness via Grills, Mathematical Recher, 59, 113-120.
  13. Roy B & Mukherjee M N, 2007, On a typical topology induced by a Grill, Soochow Journal of Math., 33, 771-786.
  14. S. Sekar & B. Jothilakshmi, 2017, “ On semi generalized star b-connectedness and semi generalized star b-compactness in Topological Spaces”, Malaya Journal of Matematik, Vol. 5, No.1, 143-148