Timeline for Given a sequence defined on the positive integers, how should it be extended to be defined at zero?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Jul 17, 2016 at 19:34 | comment | added | LSpice | Fair enough. I thought you meant that there was something wrong with the "collection of (connected / path) components" definition. | |
| Jul 17, 2016 at 6:42 | comment | added | S. Carnahan♦ | @LSpice It's been almost six years since I wrote that, but I think what I meant to say is that higher homotopy groups require pointed spaces as inputs, so if you want to define $\pi_0$ by naturally extending the definition of $\pi_n$ for $n>0$, you ought to have a pointed space as input. You are of course free to define $\pi_0$ as you like. | |
| Jul 14, 2016 at 17:53 | comment | added | LSpice | Wait, why can't $\pi_0$ be defined (as a 'bare' $\mathrm T_1$ space, or whatever $\mathrm T$ axiom gives closed points, not a pointed set) even in the absence of a base point? | |
| Oct 19, 2009 at 15:05 | history | answered | S. Carnahan♦ | CC BY-SA 2.5 |