Locally bounded set-valued mappings and monotone countable paracompactness
| Autor: | Kaori Yamazaki |
|---|---|
| Rok vydání: | 2007 |
| Předmět: |
Bounded set
Monotonically countably paracompact (MCP) Monotonic function Space (mathematics) Lower semi-continuous (l.s.c.) Combinatorics Metric space Monotone polygon Bounded function Locally bounded set-valued mappings Monotonically countably metacompact (MCM) Countable set Upper semi-continuous (u.s.c.) Paracompact space Geometry and Topology Mathematics |
| Zdroj: | Topology and its Applications. 154(15):2817-2825 |
| ISSN: | 0166-8641 |
| DOI: | 10.1016/j.topol.2007.05.015 |
| Popis: | 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 ϕ : X → B ( Y ) , a locally bounded l.s.c. mapping Φ ( ϕ ) : X → B ( Y ) with ϕ ⊂ Φ ( ϕ ) such that Φ ( ϕ ) ⊂ Φ ( ϕ ′ ) whenever ϕ ⊂ ϕ ′ , 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 ϕ : X → B ( Y ) , an l.s.c. mapping Φ ( ϕ ) : X → B ( Y ) and a u.s.c. mapping Ψ ( ϕ ) : X → B ( Y ) with ϕ ⊂ Φ ( ϕ ) ⊂ Ψ ( ϕ ) such that Φ ( ϕ ) ⊂ Φ ( ϕ ′ ) and Ψ ( ϕ ) ⊂ Ψ ( ϕ ′ ) whenever ϕ ⊂ ϕ ′ . |
| Databáze: | OpenAIRE |
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