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- W2804024175 abstract "In the realm of metric spaces we show in ZF that: (i) A metric space is compact if and only if it is countably compact and for every $varepsilon > 0$, every cover by open balls of radius $varepsilon $ has a countable subcover. (ii) Every second countable metric space has a countable base consisting of open balls if and only if the axiom of countable choice restricted to subsets of $mathbb{R}$ holds true. (iii) A countably compact metric space is separable if and only if it is second countable." @default.
- W2804024175 created "2018-06-01" @default.
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- W2804024175 date "2018-05-21" @default.
- W2804024175 modified "2023-09-26" @default.
- W2804024175 title "Some versions of second countability of metric spaces in ZF and their role to compactness" @default.
- W2804024175 doi "https://doi.org/10.14712/1213-7243.2015.229" @default.
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