Topology and statistics in zero dimensions
type: Item
instance of: scholarly article
title: Topology and statistics in zero dimensions
zbMATH Open document ID: 0806.54027
DOI: 10.1007/BF00670515
author: Charilaos N. Aneziris
published in: International Journal of Theoretical Physics
publication date: 1995-02-14T00:00:00Z
review text: The author studies finite topological \(T_ 0\)-spaces \(X\) as models for space-times. \textit{R. D. Sorkin} [Int. J. Theor. Phys. 30, No. 7, 923-947 (1991; Zbl 0733.54001)] noted that every such space carries a natural partial order denoted by ``\(\to\)'': For \(x,y \in X\), \(x \to y\) if \(x \in \Lambda (y)\) where \(\Lambda (y)\) is the intersection of all open sets containing \(y\). Using this fact it is shown how the fundamental group of the topological space \(X\) can be determined from the corresponding Hasse diagram of the partially ordered set \(X\). The last section is devoted to the study of statistics on the configuration space \((X \times X - X)/Z_ 2\) of \(X\). The idea to introduce finite topological spaces as (local) models for space-time seems to be very promising. It complements in a certain sense past contributions concerning topological spaces with a ``fundamental length'' (see, as just one example, \textit{S. P. Gudder} [SIAM J. Appl. Math. 16, 1011-1019 (1968; Zbl 0179.302)]).
Mathematics Subject Classification ID: 54F05
Mathematics Subject Classification ID: 62A01
Mathematics Subject Classification ID: 81P99
zbMATH DE Number: 575506
zbMATH Keywords: space-time models
zbMATH Keywords: fundamental group
zbMATH Keywords: finite topological spaces
reviewed by: Rudolf Z. Domiaty
MaRDI profile type: Publication
cites work: Finarity substitute for continuous topology
cites work: On the Squares of Oriented Manifolds
description: scientific article; zbMATH DE number 575506