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Lattices and their continuum limits |
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| Authors: | G Bimonte E Ercolessi G Landi F Lizzi G Sparano P Teotonio-Sobrinho |
| Institution: | a The E. Schrödinger International Institute for Mathematical Physics, Pasteurgasse 6/7, A-1090, Wien, Austria b International Centre for Theoretical Physics, P.O. Box 586, I-34100, Trieste, Italy c Dipartimento di Fisica and INFM, Università di Bologna, Via Irnerio 46, I-40126, Bologna, Italy d Dipartimento di Scienze Matematiche, Università di Trieste, P.le Europa 1, I-34127, Trieste, Italy e INFN, Sezione di Napoli, Napoli, Italy f Dipartimento di Scienze Fisiche, Università di Napoli, Mostra d' Oltremare, Pad. 19, I-80125, Napoli, Italy g Department of Physics, University of Illinois at Chicago, 60607-7059, Chicago, IL, USA |
| 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). |
| Keywords: | Continuum limit Lattices Topological spaces |
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