Arhangel’skĭı’s Solution to Alexandroff’s Problem: a Survey
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چکیده
In 1969, Arhangel’skĭı proved that for every Hausdorff space X, |X| ≤ 2χ(X)L(X). This beautiful inequality solved a nearly fifty-year old question raised by Alexandroff and Urysohn. In this paper we survey a wide range of generalizations and variations of Arhangel’skĭı’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. 1
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تاریخ انتشار 2003