Continuous Selections and Approximate Selection for Set-Valued Mappings and Applications to Metric Projections
Frank Deutsch, Petar S. Kenderov · SIAM Journal on Mathematical Analysis · 1983
Two new continuity properties for set-valued mappings are defined which are weaker than lower semicontinuity. One of these properties characterizes when approximate selections exist. A few selection theorems characterized by the other property are established. Some applications are made to set-valued metric projections.