Timeline for Name of a generalized version of semi-continuity
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 7, 2014 at 1:05 | vote | accept | Jason Siefken | ||
| Aug 6, 2014 at 16:57 | answer | added | Dave L Renfro | timeline score: 3 | |
| Aug 6, 2014 at 6:28 | comment | added | Jason Siefken | @Shamisen The property that I have used is if $(X,T)$ and $(Y,S)$ are dynamical systems with $f\circ T = S\circ f$ and $f$ is onto, then if $f$ has this property, $(X,T)$ minimal implies $(Y,T)$ is minimal. Though this follows quickly from the density property. | |
| Aug 6, 2014 at 2:07 | comment | added | Nate Eldredge | Here's a note: A sufficient condition for $f : X \to Y$ to have this property is that there is an open set $U \subset X$ such that $f$ is continuous on $U$, and $f(U) = f(X)$. If so, then on $X \setminus U$, $f$ can be as discontinuous as it likes. | |
| Aug 6, 2014 at 2:02 | comment | added | Tadashi | Just for the sake of curiosity, can you give more interesting properties of this generalization? Thanks :) | |
| Aug 5, 2014 at 22:26 | answer | added | Robert Israel | timeline score: 1 | |
| Aug 5, 2014 at 22:11 | comment | added | Robert Israel | I wouldn't call this "semi-continuity", since upper and lower semi-continuity have nothing to do with this. | |
| Aug 5, 2014 at 21:42 | comment | added | Jason Siefken | I do. The question has been corrected. | |
| Aug 5, 2014 at 21:41 | history | edited | Jason Siefken | CC BY-SA 3.0 |
added 18 characters in body
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| Aug 5, 2014 at 21:35 | comment | added | Anthony Quas | The empty set is open. Do you mean $f^{-1}U$ contains a non-empty open set whenever $U$ is a non-empty open set? | |
| Aug 5, 2014 at 20:54 | history | asked | Jason Siefken | CC BY-SA 3.0 |