关于拓扑性质的博弈论刻画的形式定义及相关开放问题的问询

Hey folks, let's unpack this question around game-theoretic characterizations of topological properties.

A few years back, a topology paper listed an open problem: it asked whether a specific property P of all topological spaces — in this case, the property of being semi-Rothberger — can be characterized game-theoretically.

Now, if someone manages to come up with a valid game-theoretic characterization for this property, the answer to that open problem is straightforwardly "yes". But here's the catch: to prove the answer is "no", we first need a rigorous, formal definition of what exactly counts as a game-theoretic characterization of a topological property.

This leads to two key follow-up questions:

• Has anyone ever formally defined this concept in a rigorous way?
• Or is this yet another one of those terms that gets thrown around in math papers without a precise, agreed-upon formal definition?

备注：内容来源于stack exchange，提问作者user107952