Linearizability of Non-expansive Semigroup Actions on Metric Spaces

Details Linearizability of Non-expansive Semigroup Actions on Metric Spaces Linearizability of Non-expansive Semigroup Actions on Metric Spaces

2006-12-19

arxiv.org/abs/math/0612553v2

Topology and its Applications 155, pp. 1576-1579, 2008

Mathematics

Metric Geometry

Scientific paper

10.1016/j.topol.2007.04.022

We show that a non-expansive action of a topological semigroup S on a metric
space X is linearizable iff its orbits are bounded. The crucial point here is
to prove that X can be extended by adding a fixed point of S, thus allowing
application of a semigroup version of the Arens-Eells linearization, iff the
orbits of S in X are bounded.

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