| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4658977 | Topology and its Applications | 2013 | 6 Pages |
Abstract
An explicit representation of the order isomorphisms between lattices of uniformly continuous functions on complete metric spaces is given. It is shown that every lattice isomorphism T:U(Y)→U(X) is given by the formula (Tf)(x)=t(x,f(τ(x))), where τ:X→Y is a uniform homeomorphism and t:X×R→R is defined by t(x,c)=(Tc)(x). This provides a correct proof for a statement made by Shirota sixty years ago.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
