2002/10/31 by Michael Megrelishvili, Lutz Schröder, Lutz Schroeder
Mathematics · #Advanced Topology and Set Theory #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GN #math.GR #msc:20M05 #msc:20M30 #msc:54D35
paper · pdf · doi:10.1016/j.topol.2004.06.006
published as Topology and Applications, Vol. 145, pp. 119-145, 2004 · New presentation of material on rewriting
openalex publication_date 2004/08/04 · arxiv created 2006/04/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
We generalize Exel's notion of partial group action to monoids. For partial monoid actions that can be defined by means of suitably well-behaved systems of generators and relations, we employ classical rewriting theory in order to describe the universal induced global action on an extended set. This universal action can be lifted to the setting of topological spaces and continuous maps, as well as to 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 and cardinality.