From 69100d84ed8305a5ecfbd61e40657956eaddc352 Mon Sep 17 00:00:00 2001 From: Chris <30360237+ccaruvana@users.noreply.github.com> Date: Thu, 17 Oct 2024 13:44:10 -0400 Subject: [PATCH] add ref to top count (#808) --- properties/P000152.md | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/properties/P000152.md b/properties/P000152.md index 34bfaa924..3ccb48d89 100644 --- a/properties/P000152.md +++ b/properties/P000152.md @@ -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}}.