ZFC existence of a countable Fréchet–Urysohn space with π-weight equal to 𝔟

Determine, within ZFC, whether there exists a countable Fréchet–Urysohn topological space whose π-weight is exactly the bounding number 𝔟.

Background

The paper constructs countable Hausdorff 0-dimensional Fréchet–Urysohn spaces that are not H-separable under the assumptions $\mathfrak b=\mathfrak c$ and $\mathfrak p=\mathfrak b$, and derives a corollary under $\mathfrak c \leq \omega_2$. These results control the π-weight in those models, but leave open what can be proved in ZFC without additional set-theoretic assumptions.

The authors explicitly note that the corollary is included because the ZFC status of whether a countable Fréchet–Urysohn space can have π-weight exactly $\mathfrak b$ is unknown. Resolving this would clarify the optimal π-weight achievable in ZFC for such spaces.