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δ-Continuous Selections of Small Multifunction

Published online by Cambridge University Press:  20 November 2018

Helga Schirmer
Helga Schirmer*
Affiliation:
Carleton University, Ottawa, Canada
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A multifunction φ : X → Y from a topological space X into a topological space Y is a correspondence such that φ(x) is a non-empty subset of Y for every x ∊ X. A single-valued function f : X → Y is called a selection of φ if f(x) ∊ φ(x) for all x ∊ X; it is called a continuous selection if f is continuous. It is well-known that not every semi-continuous or even continuous multifunction has a continuous selection (see e.g. [4] for a survey on selection theory).

We investigate here some connections between multifunctions which are 'almost single-valued” and selections which are ‘almost continuous”.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 4 , August 1972 , pp. 631 - 635
Copyright
Copyright © Canadian Mathematical Society 1972

References

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