Geodesic
δ-Continuous Selections of Small Multifunction
Canadian journal of mathematics, Tome 24 (1972) no. 4, pp. 631-635

Voir la notice de l'article provenant de la source Cambridge University Press

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”. 
Schirmer, Helga. δ-Continuous Selections of Small Multifunction. Canadian journal of mathematics, Tome 24 (1972) no. 4, pp. 631-635. doi: 10.4153/CJM-1972-058-0
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