Spaces of lower semicontinuous set-valued maps II

Abstract

Abstract This is a continuation of “Spaces of lower semicontinuous setvalued maps I”. Together, these two parts contain two interrelated main theorems. In the previous part I, the Extension Theorem is proved, which says that for binormal spaces X and Y, every bimonotone homeomorphism between C(X) and C(Y) can be extended to an ordered homeomorphism between L −(X) and L −(Y). In this part II, the Factorization Theorem is proved, which says that for binormal spaces X and Y, every ordered homeomorphism between L −(X) and L −(Y) can be characterized by a unique factorization.