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29 March 2024
 
  » arxiv » math.GN/0210024

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Globalization of Confluent Partial Actions on Topological and Metric Spaces
Michael Megrelishvili ; Lutz Schroeder ;
Date 2 Oct 2002
Subject General Topology; Group Theory MSC-class: 54D35; 20M30; 20M05 | math.GN math.GR
AffiliationBar-Ilan University, Ramat-Gam, Israel) and Lutz Schroeder (University of Bremen, Germany
AbstractGiven a partial action of a monoid on a set, equipped with a suitable system of generators and relations, we employ classical rewriting theory in order to describe the universal induced global action on a suitably extended set. This universal action can be lifted to the setting of topological spaces and continuous maps, as well as that of metric spaces and non-expansive maps. well-known constructions such as Shimrat’s homogeneous extension are special cases of this construction. We investigate various properties of the arising spaces in relation to the original space; in particular, we prove embedding theorems and preservation properties concerning separation axioms and dimension. these results imply that every normal (metric) space can be embedded into a normal (metrically) ultrahomogeneous space of the same dimension.
Source arXiv, math.GN/0210024
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