## 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.

### MSC:

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

### Keywords:

generalized continuity; closed graph
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