σ-Slicely Continuous Maps

Abstract

All examples of σ-slicely continuous maps are connected somehow with LUR Banach spaces. It is clear that if x is a denting point of a set D and Φ is a norm continuous map at x then Φ is slicely continuous at x. Hence if X is a LUR normed space then every norm continuous map Φ on BXis slicely continuous on SX.