First class selectors for upper semi-continuous multifunctions
The paper improves selection theorems for arbitrary upper-semi-continuous multifunctions due to J. Jayne and C. A. Rogers. A concept of closed-end fragmentation of a Hausdorff space helps to find a sufficiently strong result to prove the existence of first Borel class selectors for multifunctions from a metric space X to (1) a metric space Y, or (2) the Banach space Y with its weak topology. Some strengthening for separable spaces and for \(c_ 0(\Gamma)\) is made. The selector is chosen to be a \(\sigma\)-discrete function from X to Y, and it is shown that some former results easily imply that such functions are in the first Baire class if Y is ``absolute extensor for metric spaces''. It is pointed out that the author's former proof of the stronger result, with Y being the extensor for X only, was not correct. The validity of this stronger claim remained unanswered.
first Borel class selectors for multifunctions
scientific article; zbMATH DE number 4050523
scientific article