论文标题
Noetherian $π$ -bases和Telgársky的猜想
Noetherian $π$-bases and Telgársky's Conjecture
论文作者
论文摘要
我们调查Noetherian家庭，并表明每个拓扑空间都有一个Noetherian $π$ bas。我们证明，如果一个拓扑空间具有一些特殊的noetherian $π$ base，那么当nonnonnoning在BM（x）中具有胜利策略时，非Space $ x $上的Banach-Mazur游戏中有2个时光。在这种情况下，该结果涵盖了加尔文的重要定理，并且与Telgársky对此主题的猜想有关。我们的示例之一是，任何带有$πw（x）\ leqω_1$的空间$ x $都有此特殊的noetherian $π$ -base。我们对此主题提出了一些问题。
We investigate Noetherian families and show that every topological space has a Noetherian $π$-base. We prove that if a topological space has some special Noetherian $π$-bases, then NONEMPTY has a 2-tactic in the Banach-Mazur game on a space $X$, denoted as $BM(X)$, whenever NONEMPTY has a winning strategy in BM(X). This result encompasses an important theorem of Galvin in this context and is related to Telgársky's conjecture on this subject. One of our examples is that any space $X$ with $πw(X)\leq ω_1$ has this special Noetherian $π$-base. We pose some questions about this topic.
