Sequential definitions of connectedness

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 .