English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study isometric $G$-spaces and the question of when their maximalequivariant compactification is the Gromov compactification (meaning that itcoincides with the compactification generated by the distance functions topoints). Answering questions of Pestov, we show that this is the case for theUrysohn sphere and related spaces, but not for the unit sphere of the Gurarijspace.  We show that the maximal equivariant compactification of a separablycategorical metric structure $M$ under the action of its automorphism group canbe identified with the space $S_1(M)$ of 1-types over $M$, and is in particularmetrizable. This provides a unified understanding of the previous and otherexamples. In particular, the maximal equivariant compactifications of thespheres of the Gurarij space and of the $L^p$ spaces are metrizable.  We also prove a uniform version of Effros' Theorem for isometric actions ofRoelcke precompact Polish groups.

Maximal equivariant compactification of the Urysohn spaces and other metric structures