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Some weak forms of the Baire category theorem
Authors:Kyriakos Kermedis
Abstract:We show that the statement (K12) “separable, countably compact, regular spaces are Baire” is deducible from a strictly weaker form than AC, namely, CAC(?) (the axiom of choice for countable families of non‐empty subsets of the real line ?). We also find some characterizations of the axiom of dependent choices.
Keywords:Axiom of dependent choices  Baire category theorem  separable space  compact Hausdorff space
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