A note on the precompactness of weakly almost periodic groups

Details A note on the precompactness of weakly almost periodic groups A note on the precompactness of weakly almost periodic groups

2000-11-21

arxiv.org/abs/math/0011152v1

In: Nuclear groups and Lie groups, E. Martin Peinador, J. Nunez Garcia (eds.), Heldermann Verlag, 2001 (Research and Expositio

Mathematics

General Topology

7 pages, LaTeX 2e

Scientific paper

An action of a group $G$ on a compact space $X$ is called weakly almost periodic if the orbit of every continuous function on $X$ is weakly relatively compact in $C(X)$. We observe that for a topological group $G$ the following are equivalent: (i) every continuous action of $G$ on a compact space is weakly almost periodic; (ii) $G$ is precompact. For monothetic groups the result was previously obtained by Akin and Glasner, while for locally compact groups it has been known for a long time.

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