LATTICES OF LIPSCHITZ FUNCTIONS

Authors
WEAVER N
Citation
N. Weaver, LATTICES OF LIPSCHITZ FUNCTIONS, Pacific journal of mathematics, 164(1), 1994, pp. 179-193
Citations number
5
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Pacific journal of mathematics → ACNP
ISSN journal
00308730
Volume
164
Issue
1
Year of publication
1994
Pages
179 - 193
Database
ISI
SICI code
0030-8730(1994)164:1<179:LOLF>2.0.ZU;2-S
Abstract
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 di stributive. This motivates further study into the lattice structure of Lip(M) and its relation to M. We find that there is a nice duality be tween M and Lip(M) (as a lattice). We also give an abstract classifica tion of all normed vector lattices which are isomorphic to Lip(M) for some M.