Timeline for Two strengthenings of "strong measure zero"
Current License: CC BY-SA 3.0
15 events
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| May 31, 2020 at 1:54 | comment | added | bof | Your game seems to be equivalent to the Mycielski–Solovay game $G(X)$ in the paper "Strong measure zero and infinite games", Arch. Math. Logic 56 (2017), 725–732, a version of which is available for free on Arnold W. Miller's home page. They show that player II (aka "Black") has a winning strategy iff $X$ is countable (agreeing with Andreas Blass's answer) and that player I (aka "White") has a winning strategy iff $X$ does not have strong measure zero. | |
| May 30, 2020 at 3:11 | comment | added | Noah Schweber | @bof I'm not familiar with that game, but let me check ... | |
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| S Jan 10, 2016 at 22:45 | history | suggested | Boaz Tsaban |
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| Jan 10, 2016 at 22:23 | review | Suggested edits | |||
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| Oct 12, 2015 at 4:19 | history | edited | Noah Schweber | CC BY-SA 3.0 |
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| Oct 12, 2015 at 3:47 | vote | accept | Noah Schweber | ||
| Oct 12, 2015 at 3:47 | comment | added | Noah Schweber | @FrançoisG.Dorais That's a good point - this is what I get for not paying attention to the details! | |
| Sep 27, 2015 at 13:35 | comment | added | François G. Dorais | I don't think you want $Eps$ to be topologized as usual. It would be more interesting to use Baire space instead of $Eps$ and let $f \in \omega^\omega$ correspond to the sequence $\epsilon_n = 2^{-f(n)}$, for example. The issue is that $Eps = (0,\infty)^\omega$ is connected. If $x \in X$ and $X$ is csmz via $F$, we can define $H_x:Eps \to \omega$ by $H_x(f) = \mu n[x \in F(f)(n)]$. Since $\omega$ is discrete and $H_x$ is continuous, $H_x$ must be constant. If $x \neq y$, then $H_x$ and $H_y$ can't have the same constant value and it follows immediately that $X$ is countable. | |
| Sep 27, 2015 at 3:11 | comment | added | user35370 | You will probably be interested in F. Galvin's, Indeterminacy of point-open games | |
| Sep 27, 2015 at 1:33 | history | edited | Noah Schweber | CC BY-SA 3.0 |
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| Sep 26, 2015 at 9:53 | answer | added | Andreas Blass | timeline score: 21 | |
| Sep 26, 2015 at 6:41 | history | edited | Noah Schweber | CC BY-SA 3.0 |
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| Sep 26, 2015 at 6:29 | history | asked | Noah Schweber | CC BY-SA 3.0 |