Continuous ε-selection
Игорь Германович Царьков · Sbornik Mathematics · 2016
The paper is concerned with properties of sets admitting a continuous selection from the set of nearly best approximations. Necessary and sufficient conditions are put forward for the existence of continuous additive and multiplicative e-selections on closed sets. Sufficient conditions are given for the existence of continuous selections for stable set-valued mappings with not-necessarily-convex values. Bibliography: 8 titles.