Timeline for When does the set of isometries form a group?
Current License: CC BY-SA 3.0
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| Sep 17, 2011 at 20:13 | history | edited | André Henriques | CC BY-SA 3.0 |
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| Sep 17, 2011 at 20:08 | comment | added | André Henriques | Yes. I belong to that school of thought. For me, a space $X$ is connected iff it satisfies the following two conditions: any map from $\{x\in\mathbb R^1:\|x\|=1\}$ to $X$ extends to $\{x\in\mathbb R^1:\|x\|\le1\}$ and any map from $\{x\in\mathbb R^0:\|x\|=1\}$ to $X$ extends to $\{x\in\mathbb R^0:\|x\|\le1\}$. However, I also think that these confusing conventions should always be made explicit. | |
| Sep 17, 2011 at 19:54 | comment | added | Todd Trimble | There is a school of thought that says that connected spaces are nonempty by definition. (I couldn't tell from what you wrote whether you are of that school!) This is like declaring that a prime must be a non-unit; for more on this, see ncatlab.org/nlab/show/connected+space#definitions_9 | |
| Sep 17, 2011 at 18:45 | history | edited | André Henriques | CC BY-SA 3.0 |
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| Sep 17, 2011 at 18:40 | history | answered | André Henriques | CC BY-SA 3.0 |