Timeline for Is the infinite product map $(∏_{i=1}^{∞}S_{i})×f$ topologically transitive
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| Feb 19, 2019 at 16:33 | vote | accept | Safwane | ||
| Feb 11, 2019 at 18:38 | answer | added | HYL | timeline score: 2 | |
| Feb 11, 2019 at 18:27 | comment | added | YCor | Actually I'm sure of the definition of "topologically transitive" only when $f$ is a self-homeomorphism. Namely it means that for any two nonempty open subsets $U,V$ there exists $n\in\mathbf{Z}$ such that $f^n(U)\cap V$ is nonempty. | |
| Feb 11, 2019 at 18:25 | comment | added | LSpice | I just ask because the question defines "topologically mixing", but then only asks questions about "topologically transitive". I'm afraid I don't know the definition of the latter term, so, while I certainly believe @YCor's (counter)example, I can't check it myself. | |
| Feb 11, 2019 at 18:22 | comment | added | YCor | @LSpice of course not, topologically transitive is much weaker. Irrational rotation of the circle... | |
| Feb 11, 2019 at 18:22 | comment | added | Safwane | @LSpice: No, mixing imply transitive. | |
| Feb 11, 2019 at 18:22 | comment | added | LSpice | Is "topologically mixing" the same as "topologically transitive"? | |
| Feb 11, 2019 at 18:21 | comment | added | Safwane | @YCor: If you have a conterexample, then we are done | |
| Feb 11, 2019 at 18:19 | comment | added | YCor | You say that it's true for a family of 1 element, and asking about infinite families. But what about a family of two mixing maps (i.e., if $f$ is topologically transitive and $S_1,S_2$ are topologically mixing, is $S_1\times S_2\times f$ topologically transitive?) | |
| Feb 11, 2019 at 18:17 | history | edited | YCor | CC BY-SA 4.0 |
edited body
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| Feb 11, 2019 at 18:16 | comment | added | Safwane | @PiotrHajlasz: But this number is not a prime. My fovirate numbers are primes. | |
| Feb 11, 2019 at 18:13 | history | edited | Safwane | CC BY-SA 4.0 |
added 49 characters in body
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| Feb 11, 2019 at 18:13 | comment | added | Piotr Hajlasz | Congratilations! You asked a question number 100,000. | |
| Feb 11, 2019 at 18:12 | comment | added | Safwane | @YCor: Yes. I will add this in the question. | |
| Feb 11, 2019 at 18:06 | comment | added | YCor | Are you assuming that all the spaces are compact Hausdorff an that the maps are continuous? | |
| Feb 11, 2019 at 18:05 | history | edited | YCor | CC BY-SA 4.0 |
fixed typo, edited tags
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| Feb 11, 2019 at 17:43 | history | asked | Safwane | CC BY-SA 4.0 |