Assertion: global isometry | /r/CapableOf | fix $x$
Facets:
Source sentences:
text: Anyway, since for any point $x$ in Euclidean space, the group of (global) isometries fixing $x$ is isomorphic to the orthogonal group $O(n)$, it would follow, if either of the above two arguments are correct, that the local isometry group at $x$ is isomorphic to $O(n)$.