TL;DR
This paper provides criteria for extending group actions on a metric space to its compactification, with examples illustrating when these criteria are not satisfied and extension fails.
Contribution
It introduces sufficient conditions for extending group actions to compactifications and demonstrates cases where these conditions are necessary.
Findings
Established criteria for extending group actions to compactifications.
Provided examples where extension fails without meeting criteria.
Clarified the role of specific conditions in the extension process.
Abstract
We show sufficient criteria for a group of homeomorphisms acting on a metric space X to extend to one acting on a given compactification of X. We give examples for when this can fail when one of the criteria is not met.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Topology and Set Theory · Homotopy and Cohomology in Algebraic Topology