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By Mr (b: A (a, R. E. (-duke and A. Dow


A. V. Arkhangel ′ skiĭ proved that |X | ≤ 2 χ(X)L(X) for every Hausdorff space X. This beautiful inequality solved a nearly fifty-year-old question raised by Aleksandrov and Uryson. In this paper we survey a wide range of generalizations and variations of Arkhangel ′ skiĭ’s inequality. We also discuss open problems and an important legacy of the theorem: the emergence of the closure method as a fundamental unifying device in cardinal functions.

Year: 2013
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