Assuming OCA, we shall prove that for some pairs of Fréchet $\alpha_4$-spaces $X, Y$, the Fréchetness of the product $X\times Y$ implies that $X\times Y$ is $\alpha_4$. Assuming MA, we shall construct a pair of spaces satisfying the assumptions of the theorem.
@article{119325, author = {Petr Simon and Gino Tironi}, title = {No hedgehog in the product?}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {43}, year = {2002}, pages = {349-361}, zbl = {1090.54024}, mrnumber = {1922133}, language = {en}, url = {http://dml.mathdoc.fr/item/119325} }
Simon, Petr; Tironi, Gino. No hedgehog in the product?. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) pp. 349-361. http://gdmltest.u-ga.fr/item/119325/
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