Sequential definitions of connectedness

  • Çakalli H
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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.

Author-supplied keywords

  • G-sequential closure
  • G-sequential connectedness
  • G-sequential continuity
  • Sequences
  • Summability

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