G-sequentially connectedness for topological groups with operations
3rd International Conference on Analysis and Applied Mathematics, ICAAM 2016, Almaty, Kazakistan, 7 - 10 Eylül 2016, cilt.1759, (Tam Metin Bildiri)
- Yayın Türü: Bildiri / Tam Metin Bildiri
- Cilt numarası: 1759
- Doi Numarası: 10.1063/1.4959652
- Basıldığı Şehir: Almaty
- Basıldığı Ülke: Kazakistan
- Anahtar Kelimeler: G-sequentially connectedness, G-sequentially continuity, Sequences, Topological group with operations
- Maltepe Üniversitesi Adresli: Evet
Özet
It is a well-known fact that for a Hausdorff 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 G-sequential continuity, G-sequential compactness and G-sequential connectedness. In this work, we present some results about G-sequentially closures, G-sequentially connectedness and fundamental system of G-sequentially open neighbourhoods for topological group with operations which include topological groups, topological rings without identity, R-modules, Lie algebras, Jordan algebras, and many others.