Sequential definitions of connectedness

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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.

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Çakalli, H. (2012). Sequential definitions of connectedness. Applied Mathematics Letters, 25(3), 461–465. https://doi.org/10.1016/j.aml.2011.09.036

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