The development of a general theory of topological connectedness was started by Preuß (cf. [Pr1-3]) and by Herrlich [H]. Afterwards, a considerable number of papers were published on this subject and on possible generalizations of it. However, most of them used the common approach of first defining a notion of constant morphism and then using it to introduce a notion of connectedness and disconnectedness, accordingly. Castellini and Hajek in [CH] were the first ones to introduce a notion of connectedness with respect to a closure operator in a concrete category over Set.
KeywordsTopological Space Normal Subgroup Closure Operator Torsion Theory Galois Connection
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