G-Convergences of Submethods
Boletim da Sociedade Paranaense de Matematica, cilt.44, sa.5, 2026 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 44 Sayı: 5
- Basım Tarihi: 2026
- Doi Numarası: 10.5269/bspm.80335
- Dergi Adı: Boletim da Sociedade Paranaense de Matematica
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH
- Anahtar Kelimeler: G-convergence, Gs-closed subset, GY-convergence
- Erciyes Üniversitesi Adresli: Evet
Özet
Classical topological notions such as openness, closedness, and continuity can be expressed in sequential form, particularly in the case of first-countable Hausdorff spaces. Motivated by this idea, a generalized convergence method known as the G-method, has been introduced. Different studies related to the G-method have been widely explored in recent literature, including studies on G-continuity, G-compactness, and other related topological properties. In this study, the theory of the G-method defined on a set X is extended by introducing the concept of G-submethod GY, induced on a non-empty subset Y⊆ X. We examine the behaviours of G-open and G-closed subsets under these submethods. Several characterizations are provided to determine when GY-closedness and GY-openness are preserved within submethods. In addition, we also investigate the preservation of topological properties such as G-compactness, and separation axioms G-T0, G-T1, and G-Hausdorff for G-submethods.