G-compactness and local g-compactness of topological groups with operations
4th International Conference of Mathematical Sciences, ICMS 2020, İstanbul, Türkiye, 17 - 21 Haziran 2020, cilt.2334, (Tam Metin Bildiri)
- Yayın Türü: Bildiri / Tam Metin Bildiri
- Cilt numarası: 2334
- Doi Numarası: 10.1063/5.0042236
- Basıldığı Şehir: İstanbul
- Basıldığı Ülke: Türkiye
- Anahtar Kelimeler: G-sequential compactness, Local g-compactness, Topological group with operations
- Maltepe Üniversitesi Adresli: Evet
Özet
It is well known that for a Hausdor_topological group X, the limits of convergent sequences in X define a function denoted by lim from the set of all convergent sequences in X to X. This notion has been modified by Connor and Grosse-Erdmann for real functions by replacing lim with an arbitrary linear functional G defined on a linear subspace of the vector space of all real sequences. Recently some authors have extended the concept to the topological group setting and introduced the concepts of Gcontinuity, G-compactness and G-connectedness. In this paper we prove some results about G-compactness for topological group with operations which include topological groups, topological rings without identity, R-modules, Lie algebras, Jordan algebras, and many others.