Is there an example of a nonempty bounded subset of the Euclidean plane which has an infinite isometry group?
Would the unit cube $[0,1]^n$ be an example?
2025-01-12 23:42:50.1736725370
Infinite isometry in subset of Euclidean plane
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Try a circle.
$[0,1]^n$ is not a subset of the Euclidean plane, and its isometry group (for any norm) is finite. It is nonempty and bounded, though.