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Fréchet-Urysohn space; $\langle\alpha_4\rangle$-space; Martin's Axiom; almost disjoint functions; double iterated power
Assuming Martin's Axiom, we provide an example of two Fréchet-Urysohn $\langle\alpha_4\rangle$-spaces, whose product is a non-Fréchet-Urysohn $\langle\alpha_4\rangle$-space. This gives a consistent negative answer to a question raised by T. Nogura.
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