Gn-methods and Gn-compactness via nets
Georgian Mathematical Journal, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2026
- Doi Numarası: 10.1515/gmj-2026-3028
- Dergi Adı: Georgian Mathematical Journal
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Academic Search Ultimate (EBSCO)
- Anahtar Kelimeler: Gn-compactness, Gn-continuity, Gn-convergence, Gn-methods, Nets
- Erciyes Üniversitesi Adresli: Evet
Özet
Sequences, or more generally, nets, are important in numerous branches of mathematics, such as analysis, number theory and topology. For the reasons explained in introduction, in some works we move from sequences to nets. Considering limits of sequences in a Hausdorff space X assigns a function lim from the set c(X) of convergent sequences to X. Inspired by this, a G-method, as a generalization of the function lim, is defined by replacing the set c(X) with a certain class of sequences. Originated by such G-methods, the sequential versions of some fundamental properties in topology, such as continuity, compactness, and connectedness, have been recently generalized by G-methods defined for sequences in sets. This paper presents a study of convergent Gn-methods involving nets rather than sequences as generalizations of G-methods; and then gives some properties and characterizations of Gn-compactness and Gn-countably compactness.