Abstract
This chapter starts with the Heine–Borel theorem and its characterization of complete orders, and then uses Borel’s theorem to give a measure-theoretic proof that \(\mathbf{R}\) is uncountable. Other topics focus on measure and category: Lebesgue measurable sets, Baire category, the perfect set property for \(\mathcal{G}_{\delta }\) sets, the Banach–Mazur game and Baire property, and the Vitali and Bernstein constructions.
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Dasgupta, A. (2014). The Heine–Borel and Baire Category Theorems. In: Set Theory. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4614-8854-5_15
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DOI: https://doi.org/10.1007/978-1-4614-8854-5_15
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Publisher Name: Birkhäuser, New York, NY
Print ISBN: 978-1-4614-8853-8
Online ISBN: 978-1-4614-8854-5
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