G-Connectedness in Topological Groups with Operations
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 $G$-sequential continuity, $G$-sequential compactness and $G$-sequential connectedness. In this paper we present some results about $G$-sequentially closures, $G$-sequentially connectedness and fundamental system of $G$-sequentially 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.
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