Globalization of Confluent Partial Actions on Topological and Metric Spaces

Details Globalization of Confluent Partial Actions on Topological and Metric Spaces Globalization of Confluent Partial Actions on Topological and Metric Spaces

2002-10-02

arxiv.org/abs/math/0210024v2

Topology and Applications, Vol. 145, pp. 119-145, 2004

Mathematics

General Topology

New presentation of material on rewriting

Scientific paper

10.1016/j.topol.2004.06.006

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.

Affiliated with

Also associated with

No associations

Rating

Globalization of Confluent Partial Actions on Topological and Metric Spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Globalization of Confluent Partial Actions on Topological and Metric Spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Globalization of Confluent Partial Actions on Topological and Metric Spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-165152