G-Connectedness in Topological Groups with Operations

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MUCUK O., Cakalli H.

FILOMAT, vol.32, no.3, pp.1079-1089, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 3
  • Publication Date: 2018
  • Doi Number: 10.2298/fil1803079m
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1079-1089
  • Erciyes University Affiliated: Yes

Abstract

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-continuity, G-compactness and G-connectedness. In this paper we present some results about G-hulls, G-connectedness and G-fundamental systems of G-open neighbourhoods for a wide class of topological algebraic structures called groups with operations, which include topological groups, topological rings without identity, R-modules, Lie algebras, Jordan algebras, and many others.