On a simultaneous selection theorem

Abstract

Valov proved a general version of Arvanitakis's simultaneous selection theorem which is a common generalization of both Michael's selection theorem and Dugundji's extension theorem. We show that Valov's theorem can be extended by applying an argument by means of Pettis integrals due to Repovš, Semenov and Shchepin.

A simultaneous selection theorem

“…Recently, V. Valov [16] obtained an interesting generalization of Theorem 1.1 using a different proof, and T. Yamauchi [17], basing on this proof, dropped the assumption of X being a k-space and also gave some applications of the theorem.…”