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- W2037915087 abstract "We characterize Lindelöf p -spaces which are absolute extensors for zero-dimensional perfectly normal spaces. As an application we prove that a Lindelöf Čech-complete space X is an absolute extensor for zero-dimensional spaces if and only if there exists an upper semi-continuous compact-valued map r : X 3 → X such that r ( x, y, y ) = r ( y, y, y ) = x for all , y ε X . This result is new even when applied to compact spaces and yields the following new characterization of Dugundji spaces: A compact Hausdorff space X is Dugundji if and only if there exists an upper semi-continuous compact-valued map r : X 3 → X such that r ( x, y, y ) = r ( y, y, x ) = x for all x, y ε X . It is worth noting that, by a result of Uspenskij, in the above characterization of Dugundji spaces the set-valued map r cannot be replaced by a single-valued (continuous) map, the 5-dimensional sphere S 5 being a counterexample." @default.
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- W2037915087 date "1996-12-01" @default.
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- W2037915087 title "A characterization of Dugundji spaces via set-valued maps" @default.
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- W2037915087 doi "https://doi.org/10.1016/s0166-8641(96)00049-1" @default.
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