Timeline for Finding paths in a path connected space
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Mar 24, 2011 at 11:10 | comment | added | Thierry Zell | I'm assuming that region implies open (otherwise it's easy to create problems). In that case, Daniel Litt's solution sounds pretty solid to me. Making the path n times differentiable should not be a problem. | |
| Mar 24, 2011 at 10:07 | comment | added | Mark Grant | The Hahn–Mazurkiewicz theorem says that, under mild topological assumptions on $E$, there exists a surjective path (see en.wikipedia.org/wiki/Space-filling_curve). Of course these space-fillers may be extremely non-differentiable. | |
| Mar 24, 2011 at 7:58 | comment | added | S. Carnahan♦ | What do you mean when you say "region"? | |
| Mar 24, 2011 at 7:15 | comment | added | Ganesh | @Daniel: How do we connect points when $P$ has to be $n$-times differentiable? | |
| Mar 24, 2011 at 7:06 | comment | added | Daniel Litt | $P$ always exists---take a countable dense subset of $E$, enumerate it, and connect the points in order... | |
| Mar 24, 2011 at 7:03 | history | edited | Ganesh | CC BY-SA 2.5 |
added 456 characters in body
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| Mar 24, 2011 at 6:52 | history | asked | Ganesh | CC BY-SA 2.5 |