Timeline for Sufficient conditions for continuity of function $y\mapsto\min_{[x_0,y]}\phi$
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 12, 2013 at 20:43 | comment | added | user26107 | $\forall \epsilon > 0$, $\exists \delta > 0$, $\forall x \in (x_0-\delta, x_0+\delta)$: $\phi(x) \in (\phi(x_0)-\epsilon, \phi(x_0)+\epsilon)$. So $\psi(y) \in (\phi(x_0)-\epsilon, \phi(x_0)+\epsilon)$ too, therefore $\psi(y) \to \phi(x_0)$. The same is true for all other points. | |
| Apr 12, 2013 at 19:27 | history | edited | user22980 | CC BY-SA 3.0 |
added 153 characters in body; added 24 characters in body
|
| Apr 12, 2013 at 19:25 | comment | added | user22980 | You are right, the counter-example is not valid. So maybe there is no need of further assumption? | |
| Apr 12, 2013 at 19:18 | comment | added | qianzhang | At the beginning you assumed that $\phi$ is continuous everywhere, but in your example $\phi$ is discontinuous at $0$, why? | |
| Apr 12, 2013 at 19:12 | history | asked | user22980 | CC BY-SA 3.0 |