Sequential definitions of connectedness

Abstract

We investigate the impact of changing the definition of convergence of sequences on the structure of the set of connected subsets of a topological group, X. A non-empty subset A of X is called G-sequentially connected if there are no non-empty and disjoint G-sequentially closed subsets U and V, both meeting A, such that A⊆U∪V. Sequential connectedness in a topological group is a special case of this generalization when G=lim. © 2011 Elsevier Ltd. All rights reserved.