c-continuity and closed graphs. (English) Zbl 0589.54027

A type of generalized continuity usually called c-continuity is extended to multivalued mappings. A multivalued mapping is called upper c-semi- continuous at \(p\in X\) if for any open V containing F(p) and such that Y- V is compact, there exists a neighbourhood U of p such that F(x)\(\subset V\) for any \(x\in U\). It is proved that for sufficiently general topological spaces a multivalued mapping is upper c-semi-continuous exactly if it is with a closed graph. A related type of continuity and its connection to the notion of closed graph is also studied.


54C60 Set-valued maps in general topology
54C08 Weak and generalized continuity
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