Timeline for A question regarding Danskin's theorem
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 27, 2012 at 17:21 | comment | added | Stewart | Thanks! I understand I might have underrated the importance of this website with my ignorance - my apologies. | |
| Apr 27, 2012 at 17:09 | comment | added | Lee Mosher | Yes. All that is relevant to make this argument work is that $\phi : X \cross Z \to \R$ is continuous, $X$ is a topological space, and $Z$ is a compact topological space. Consult any introductory book on topology. | |
| Apr 27, 2012 at 16:58 | comment | added | Stewart | I believe you are right, thanks. Do you know if the continuity is maintained when in addition one imposes that ${\bf x} \in {\bf X}$ where $\bf X$ is (non-empty) compact and convex? | |
| Apr 27, 2012 at 16:55 | comment | added | Lee Mosher | For purposes of continuity of $f$, convexity is irrelevant, and Danskin's theorem is irrelevant. As $\bf x$ varies, the compact subsets $\phi({\bf x},Z)$ vary continuously in the Hausdorff metric on compact subsets of $\bf R$, and so their maxima vary continuously. But, this is really a question for math.stackexchange.com, not MO. | |
| Apr 27, 2012 at 16:42 | history | edited | Stewart | CC BY-SA 3.0 |
added 12 characters in body
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| Apr 27, 2012 at 16:31 | history | asked | Stewart | CC BY-SA 3.0 |