3 problems

A topological space is Baire if every countable intersection of open dense subsets is dense. An $\mathcal{N}$-space is the class of spaces defined in the source. Christensen's conj…

Let $X$ be a Tychonoff space. A family of subsets of $X$ is moving off if for every compact set $K\subset X$ it contains a nonempty member disjoint from $K$. The space $X$ has the…

Let $X$ be a topological space, let $\pi(X)$ be the least cardinality of a $\pi$-base for $X$, and let $\operatorname{BM}(X)$ denote the Banach–Mazur game on $X$. For positive card…