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Lattices of Lipschitz
functions
Nikolai Isaac Weaver |
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Vol. 164 (1994), No. 1, 179–193
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Abstract |
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Let M be a metric space. We observe that 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 Lip(M) and its relation to M. We find that there is a nice duality between M and Lip(M) (as a lattice). We also give an abstract classification of all normed vector lattices which are isomorphic to Lip(M) for some M. |
Mathematical Subject Classification 2000
Primary: 46B42
Secondary: 46B25, 46E15
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Milestones
Received: 20 March 1992
Revised: 30 March 1993
Published: 1 May 1994
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Authors |
| Nikolai Isaac Weaver | |
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