G-Connectedness in Topological Groups with Operations

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MUCUK O. , Cakalli H.

FILOMAT, cilt.32, ss.1079-1089, 2018 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 32 Konu: 3
  • Basım Tarihi: 2018
  • Doi Numarası: 10.2298/fil1803079m
  • Dergi Adı: FILOMAT
  • Sayfa Sayısı: ss.1079-1089


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.