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- W2118875400 abstract "For a compact metric space ( X , d ) , we use ↓ USC ( X ) and ↓ C ( X ) to denote the families of the regions below of all upper semi-continuous maps and the regions below of all continuous maps from X to I = [ 0 , 1 ] , respectively. In this paper, we consider the two spaces topologized as subspaces of the hyperspace Cld ( X × I ) consisting of all non-empty closed sets in X × I endowed with the Vietoris topology. We shall show that ↓ C ( X ) is Baire if and only if the set of isolated points is dense in X , but ↓ C ( X ) is not a G δ σ -set in ↓ USC ( X ) unless X is finite. As the main result, we shall prove that if X is an infinite locally connected compact metric space then ( ↓ USC ( X ) , ↓ C ( X ) ) ≈ ( Q , c 0 ) , where Q = [ − 1 , 1 ] ω is the Hilbert cube and c 0 = { ( x n ) ∈ Q : lim n → ∞ x n = 0 } ." @default.
- W2118875400 created "2016-06-24" @default.
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- W2118875400 date "2006-09-01" @default.
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- W2118875400 title "The hyperspace of the regions below of continuous maps is homeomorphic to <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:msub><mml:mi>c</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math>" @default.
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- W2118875400 doi "https://doi.org/10.1016/j.topol.2005.12.009" @default.
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