Michael's theory of continuous selections. Development and applications

Abstract

CONTENTS Introduction §1. Basic ideas and formulations of the main theorems §2. Applications of the theory of continuous selections §3. Proofs of the main theorems. Selection characteristics of paracompactness and of properties of normality type §4. Generalizations of the main selection theorems. The method of covers. Theorems on "the modulus of countable sets". Amalgamated selection theorems §5. Attempts to waive convexity. Convexity in metric spaces. Paraconvexity. Topological convexity §6. Selections and averaging operators. The universality of the 0-dimensional selection theorem §7. Miscellaneous results References