Geodesic
No hedgehog in the product?
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 2, pp. 349-361.

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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.
Classification : 03E50, 03E65, 54B10, 54D55, 54G20
Keywords: Fréchet space; $\alpha _4$-space; Fréchet fan; $(\kappa, \kappa )$-good set 
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Simon, Petr; Tironi, Gino. No hedgehog in the product?. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 2, pp. 349-361. http://geodesic.mathdoc.fr/item/CMUC_2002__43_2_a12/