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- W2100378427 abstract "A set-valued mapping Φ : X → 2 Y acting between topological spaces X and Y is said to be “lower demicontinuous” if the interior of the closure of the set Φ −1 ( V ): = { x ∈ X : Φ( x ) ∩ V ≠ ∅} is dense in the closure of Φ −1 ( V ) for each open set V in Y . Čoban, Kenderov and Revalski (1994) showed that for every densely defined lower demicontinuous mapping Φ acting from a Baire space X into subsets of a monotonely Čech-complete space Y , there exist a dense and G δ subset X 1 ⊆ X and an usco mapping G : X 1 → 2 Y such that G ( x ) ⊆ Φ*( x ), for every x ∈ X 1 , where the mapping Φ*: X → 2 Y is the extension of Φ defined by, W is a neighbourhood of x }. In this paper we present a proof of the above result with the notion of monotone Čcech-completeness replaced by the weaker notion of partition completeness. In addition, we observe that if the range space also lies is Stegall's class then we may assume that the mapping G is single-valued on X 1 ." @default.
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- W2100378427 date "2002-04-01" @default.
- W2100378427 modified "2023-09-26" @default.
- W2100378427 title "Usco selections of densely defined set-valued mappings" @default.
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- W2100378427 doi "https://doi.org/10.1017/s0004972700020347" @default.
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