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add ref to top count (#808)
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ccaruvana authored Oct 17, 2024
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Expand Up @@ -9,11 +9,13 @@ refs:
name: Limited information strategies and discrete selectivity (Clontz & Holshouser)
- mathse: 4737285
name: Do uncountable spaces admit Markov strategies in Rothberger-style games?
- doi: 10.4995/agt.2024.21437
name: On traditional Menger and Rothberger variations (Caruvana, Clontz, Holshouser)
---
Markov Rothberger: The second player has a Markov winning strategy in the Rothberger game $\mathsf{G}_1(\mathcal O_X,\mathcal O_X)$ (relying on only the round number and most recent move of the opponent). See pages 2 and 3 of {{doi:10.1016/j.topol.2019.07.008}} for more details.

Markov $\Omega$-Rothberger: The second player has a Markov winning strategy in the game $\mathsf{G}_1(\Omega_X,\Omega_X)$ (relying on only the round number and most recent move of the opponent). See pages 2 and 3 of {{doi:10.1016/j.topol.2019.07.008}} for more details.

Topologically countable: If there is $\{ x_n : n \in \omega \} \subseteq X$ so that, for every $x \in X$, there is some $n \in \omega$ so that every neighborhood of $x_n$ contains $x$.
Topologically countable: If there is $\{ x_n : n \in \omega \} \subseteq X$ so that, for every $x \in X$, there is some $n \in \omega$ so that every neighborhood of $x_n$ contains $x$. See {{doi:10.4995/agt.2024.21437}} for more on this property.

These are all shown to be equivalent at {{mathse:4737285}}.
These are all shown to be equivalent in Theorem 4.17 of {{doi:10.4995/agt.2024.21437}} and also at {{mathse:4737285}}.

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