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No hedgehog in the product? (English) Zbl 1090.54024
Summary: 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.

##### MSC:
 54D55 Sequential spaces 54B10 Product spaces in general topology 54G20 Counterexamples in general topology
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