Products of Compact Spaces and the Axiom of Choice
نویسندگان
چکیده
We study the Tychonoff Compactness Theorem for several different definitions of a compact space.
منابع مشابه
Products , the Baire category theorem , and the axiom of dependent choice
In ZF (i.e., Zermelo-Fraenkel set theory without the Axiom of Choice) the following statements are shown to be equivalent: (1) The axiom of dependent choice. (2) Products of compact Hausdorff spaces are Baire. (3) Products of pseudocompact spaces are Baire. (4) Products of countably compact, regular spaces are Baire. (5) Products of regular-closed spaces are Baire. (6) Products of Čech-complete...
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This is a continuation of [dhhkr]. We study the Tychonoff Compactness Theorem for various definitions of compact and for various types of spaces, (first and second countable spaces, Hausdorff spaces, and subspaces of R). We also study well ordered Tychonoff products and the effect that the multiple choice axiom has on such products.
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The stability of the Lindelöf property under the formation of products and of sums is investigated in ZF (= Zermelo-Fraenkel set theory without AC, the axiom of choice). It is • not surprising that countable summability of the Lindelöf property requires some weak choice principle, • highly surprising, however, that productivity of the Lindelöf property is guaranteed by a drastic failure of AC, ...
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ورودعنوان ژورنال:
- Math. Log. Q.
دوره 48 شماره
صفحات -
تاریخ انتشار 2002