Hypographs of Upper Semi-continuous Maps and Continuous Maps on a Bounded Open Interval

Abstract

For any bounded open interval X in the Euclidean space E 1 , let ↓USC(X) and ↓C(X) be the families of all which is not homeomorphic to (s, c 0). Hence this paper figures out the topological structure of the pair (↓USC(X), ↓C(X)).