Let $f$ be a real-valued baire class $\xi$ function.
In this paper, page $24$, section $5$, before remark $5.1$, the author defined the set
$T_{f,\xi}=\{ \tau^{\prime} : \tau^{\prime} \supseteq \tau \text{ Polish}, \tau^{\prime} \subseteq \sum_{\xi}^0 (\tau), f \in B_1(\tau^{\prime})\}$
The set $T_{f,\xi}$ contains all topologies which convert $f$ into a Baire class one function.
Question: Can the set $T_{f, \xi}$ be infinite? I want to know this because I am trying to see whether the definition $5.3$ can attain its minimum or not.