Timeline for Continuity of a homotopy-like function
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 7, 2011 at 14:41 | history | edited | Jeff Strom | CC BY-SA 3.0 |
changed $g(y)$ to $g(x)$
|
| Nov 7, 2011 at 13:19 | vote | accept | Chulumba | ||
| Nov 7, 2011 at 11:45 | comment | added | Buschi Sergio | In your example you make merely a funtion $F$ such that for any $t$ the function $F_t: x \mapsto F(x, t)$ is contnuous, of course this is too weak for have the (global) continuity of $F$. Anyway if you parametrize the paths by the homotopy contraction maps you get a (continuous) homotopy $F$ from $f$ to $g$. Let $G: X \times I\to Y: 1_Y\ \tilde\ \ C(y_0)$ (contraction homotopy from identity map to costant map on the point $y_0$). then join the maps $F(x, t):= G(f(x), 2t)\ t\in[0,1/2]$ and $F(x, t):= G(g(x), 2-2t)\ t\in[1/2,1]$ . | |
| Nov 7, 2011 at 10:47 | answer | added | Martin Brandenburg | timeline score: 3 | |
| Nov 7, 2011 at 10:38 | history | asked | Chulumba | CC BY-SA 3.0 |