Abstract
We study the notions of continuity and cliquishness of mapsf: (X, T)→(Y,T′) with the help of collections η⊂P(P(Y)) of families such that the conditionK⊂A∈A impliesK∈A for eachA∈ η andK⊂Y. The article points to far-going similarities between the weak forms of continuity, strong forms of continuity and cliquishness. The present concept unifis various concepts of continuity and cliquishness of maps.
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