✦ LIBER ✦

Countable choice and pseudometric spaces

✍ Scribed by H.L. Bentley; H. Herrlich

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 672 KB
Volume: 85
Category: Article
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(97)00138-7

No coin nor oath required. For personal study only.

✦ Synopsis

In the realm of pseudometric spaces the role of choice principles is investigated. In particular it is shown that in ZF (i.e., Zermelo-Fraenkel set theory without the axiom of choice) the axiom of countable choice is not only sufficient but also necessary to establish each of the following results:

separable -countable base, 2. separable -LindelGf, 3. separable ti topologically totally bounded, 4. compact + separable, 5. separability is hereditary, 6. the Baire Category Theorem for complete spaces with countable base, 7. the Baire Category Theorem for complete, totally bounded spaces, 8. compact -sequentially compact, 9. compact -(totally bounded and complete), IO. sequentially compact -(totally bounded and complete), 1 1. WeierstraD compact -(totally bounded and complete).

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