On <i>G</i>-Compactness of Topological Groups with Operations

MUCUK O., Cakalli H.

FILOMAT, cilt.36, sa.20, ss.7113-7121, 2022 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 36 Sayı: 20
  • Basım Tarihi: 2022
  • Doi Numarası: 10.2298/fil2220113m
  • Dergi Adı: FILOMAT
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.7113-7121
  • Anahtar Kelimeler: Sequences, G-compactness, G-hull, G-continuity, G-connectedness, topological group with operations
  • Erciyes Üniversitesi Adresli: Evet

Özet

One can notice that if X is a Hausdorff space, then limits of convergent sequences in X give us a function denoted by lim from the set of all convergent sequences in X to X. This notion has been extended by Connor and Grosse-Erdmann to an arbitrary linear functional G defined on a subspace of the vector space of real numbers. Following this idea some authors have defined concepts of G-continuity, G-compactness and G-connectedness in topological groups. In this paper we present some results about G-compactness of topological group with operations such as topological groups, topological rings without identity, R-modules, Lie algebras, Jordan algebras and many others.