A unified approach to generalized continuities
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CitationMatejdes, M. (2009). A unified approach to generalized continuities. Maltepe Üniversitesi. s. 271.
Contribution deals with a concept which covers many known types of continuities. Method is based on stating appropriate system E of subsets on domain. The first motivation for introducing comes from definition of quasi continuity. Namely, a mapping f : X → Y is E-continuous at x, if for any open sets V and U such that x ∈ U and f(x) ∈ V , there is a set E ∈ E, such that E ⊂ U ∩ f −1 (V ). The next, stronger variant, is generalization of continuity. A function f is dense E-continuous at x, if for any open set V containing f(x), there is an open set U 3 x, such that for any open set H ⊂ U, there is a set E ∈ E such that E ⊂ H ∩ f −1 (V ). When E is system of all non-empty open sets, it is equivalent to the notion of quasi continuity or (dense variant) α-continuity. Using different systems E, we are able to describe many types of continuities. Approach is used in function as well as multifunction setting.
SourceInternational Conference of Mathematical Sciences
- Makale Koleksiyonu 
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