A generic factorization theorem

摘要: Let F : Z → X be a minimal usco map from the Baire space into compact . Then complete metric P and G can constructed so that for every dense δ -subset 1 of there exist (single-valued) continuous f such ( )⊂ z )) ∈Z In particular, if is single valued on , then also single-valued its domain. The above theorem remains valid Cech an arbitrary completely regular space. These factorization theorems show some generalizations Namioka concerning generic single-valuedness continuity mappings defined in more general spaces derived similar results with domains. used as tool to establish certain topological contain metrizable subspaces.