G-Compactness and Local G-Compactness of Topological Groups with Operations

Mucuk O., Cakalli H.

4th International Conference of Mathematical Sciences (ICMS), ELECTR NETWORK, 17 - 21 Haziran 2020, cilt.2334 identifier identifier identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 2334
  • Doi Numarası: 10.1063/5.0042236
  • Basıldığı Ülke: ELECTR NETWORK
  • Anahtar Kelimeler: G-sequential compactness, local G-compactness, topological group with operations, CROSSED-MODULES, INTERNAL CATEGORIES, CONTINUITY, COVERINGS
  • Erciyes Üniversitesi Adresli: Evet

Özet

It is well known 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 $G$-continuity, $G$-compactness and $G$-connectedness. In this paper we prove some results on different types of $G$-compactness for topological group with operations which include topological groups, topological rings without identity, R-modules, Lie algebras, Jordan algebras, and many others.