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Lattices and their continuum limits

Authors
Journal
Journal of Geometry and Physics
0393-0440
Publisher
Elsevier
Publication Date
Volume
20
Issue
4
Identifiers
DOI: 10.1016/s0393-0440(95)00063-1
Keywords
  • Continuum Limit
  • Lattices
  • Topological Spaces
Disciplines
  • Mathematics

Abstract

Abstract 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).

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