Subcontinuity |
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Authors: | ?ubica Holá Branislav Novotný |
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Institution: | 1.Mathematical Institute,Slovak Academy of Sciences,Bratislava,Slovakia |
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Abstract: | We give interesting characterizations using subcontinuity. Let X, Y be topological spaces. We study subcontinuity of multifunctions from X to Y and its relations to local compactness, local total boundedness and upper semicontinuity. If Y is regular, then F is subcontinuous iff `(F)]\bar F is USCO. A uniform space Y is complete iff for every topological space X and for every net {F
a
}, F
a
⊂ X × Y, of multifunctions subcontinuous at x ∈ X, uniformly convergent to F, F is subcontinuous at x. A Tychonoff space Y is Čech-complete (resp. G
m-space) iff for every topological space X and every multifunction F ⊂ X × Y the set of points of subcontinuity of F is a G
δ
-subset (resp. G
m-subset) of X. |
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Keywords: | |
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