Lattices of Lipschitz functions (Q1326974)
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scientific article; zbMATH DE number 589814
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Lattices of Lipschitz functions |
scientific article; zbMATH DE number 589814 |
Statements
Lattices of Lipschitz functions (English)
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10 October 1994
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Let \(M\) be a metric space. We observe that \(\text{Lip}(M)\) has a striking lattice structure: its closed unit ball is lattice-complete and completely distributive. This motivates further study into the lattice structure of \(\text{Lip}(M)\) and its relation to \(M\). We find that there is a nice duality between \(M\) and \(\text{Lip}(M)\) (as a lattice). We also give an abstract classification of all normed vector lattices which are isomorphic to \(\text{Lip}(M)\) for some \(M\).
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lattice structure of \(\text{Lip}(M)\)
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duality between \(M\) and \(\text{Lip}(M)\) (as a lattice)
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Lipschitz spaces
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complete distributivity
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closed unit ball is lattice-complete and completely distributive
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normed vector lattices
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