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, XX. A non-empty subset AA of XX is called GG-sequentially connected if there are no non-empty and disjoint GG-sequentially closed subsets UU and VV, both meeting A, such that A⊆U⋃VA⊆U⋃V. Sequential connectedness in a topological group is a special case of this generalization when G=lim.