This is a continuation of a€?Spaces of lower semicontinuous setvalued maps Ia€?. 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 a?’(X) and L a?’(Y). In this part II, the Factorization Theorem is proved, which says that for binormal spaces X and Y, every ordered homeomorphism between L a?’(X) and L a?’(Y) can be characterized by a unique factorization.
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