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Continuous selections of finite-set valued mappings. (English) Zbl 0769.54021
This paper deals with the existence of continuous selections for finite- valued continuous multifunctions. Main theorem: Let $$X$$ be a locally connected treelike space and $$Y$$ a Hausdorff topological space. Then each continuous finite-valued mapping $$F: X\to 2^ Y$$ admits continuous selections in the strong sense (i.e. you can choose a point in the graph). A counterexample shows that hereditary unicoherence of $$X$$ is necessary. It is shown that “treelike” and “hereditarily unicoherent” are equivalent for various subclasses of connected and locally connected spaces.
Reviewer: C.R.Borges (Davis)
##### MSC:
 54C65 Selections in general topology
Full Text:
##### References:
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