Locally bounded set-valued mappings and monotone countable paracompactness |
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Authors: | Kaori Yamazaki |
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Institution: | Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan |
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Abstract: | We prove that the following statements are equivalent for a space X: (1) X is monotonically countably paracompact; (2) for every metric space Y there exists an operator Φ assigning to each locally bounded mapping , a locally bounded l.s.c. mapping with ?⊂Φ(?) such that Φ(?)⊂Φ(?′) whenever ?⊂?′, where B(Y) is the set of all non-empty closed bounded sets of Y; (3) for every metric space Y, there exist operators Φ and Ψ assigning to each u.s.c. mapping , an l.s.c. mapping and a u.s.c. mapping with ?⊂Φ(?)⊂Ψ(?) such that Φ(?)⊂Φ(?′) and Ψ(?)⊂Ψ(?′) whenever ?⊂?′. |
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Keywords: | 54C30 54C60 54D15 54E20 46A99 47H04 |
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