Lattices and their continuum limits

✍ Scribed by G. Bimonte; E. Ercolessi; G. Landi; F. Lizzi; G. Sparano; P. Teotonio-Sobrinho

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 842 KB
• Volume: 20
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(95)00063-1

✦ Synopsis

We address the problem of the continuum limit for a system of Hausdorff lattices (namely lattices of isolated points) approximating a topological space M. The correct framework is that of projective systems. The projective limit is a universal space from which M can be recovered as a quotient. We dualize the construction to approximate the algebra C(M) of continuous functions on M. In a companion paper we shall extend this analysis to systems of noncommutative lattices (non-Hausdorff lattices).