Timeline for When does the set of isometries form a group?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 17, 2011 at 18:10 | comment | added | Andreas Blass | The Riemannian manifolds in the answer are tacitly assumed to be connected. | |
| Sep 17, 2011 at 16:46 | comment | added | Edmund Harriss | I agree that surjectivity is all that is required for the isometry; however the question asks what properties of the metric space make it unecessary to assume that isometries are surjective. | |
| Sep 17, 2011 at 16:37 | comment | added | Noam D. Elkies | Much simpler counterexamples: the positive or nonnegative reals, or the natural numbers, with the shift $x \mapsto x+1$; or any infinite space with the discrete metric and any map at all that's injective but not surjective. | |
| Sep 17, 2011 at 16:35 | history | answered | Keivan Karai | CC BY-SA 3.0 |