There are two metric Baire spaces, whose product is not Baire; a counterexample is given in the slides [An absolute barely Baire space][1], L.F. Aurichi and G.A.A. Medina, 2020. We present Fleissner and Kunen's proof with applications of Clubs and stationary sets in $\omega_{1}$.

<cite authors="Fleissner, W. G.; Kunen, K.">_Fleissner, W. G.; Kunen, K._, [**Barely Baire spaces**](http://dx.doi.org/10.4064/fm-101-3-229-240), Fundam. Math. 101, 229-240 (1978). [ZBL0413.54036](https://zbmath.org/?q=an:0413.54036).</cite>

  [1]: https://drive.google.com/file/d/1ecALwzNmtiPHekEqFBHik8kfmLvSFy1Y/view?usp=sharing