Arhangel'ski?'s solution to Alexandroff's problem: A survey |
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Authors: | RE Hodel |
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Institution: | Department of Mathematics, Duke University, Durham, NC 27708, USA |
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Abstract: | In 1969, Arhangel'ski? proved that |X|?2χ(X)L(X) for every Hausdorff space 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'ski?'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. |
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Keywords: | 54A25 54A35 |
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