What do finite, infinite, countable, not countable, countably infinite mean? [duplicate] Ask Question Asked 13 years, 3 months ago Modified 13 years, 3 months ago

Nov 14, 2021 · In second-countable spaces—as in metric spaces—compactness, sequential compactness, and countable compactness are all equivalent properties. Question: So apparently, …

Mar 16, 2015 · The definition for 2nd countable topological space is that "the topological space has a countable basis." My confusion is whether or not they mean countably infinite basis only.

Nov 25, 2015 · If you can achieve a bijection of the members of the sets to $\Bbb N$, the the set will be called countable, and moreover ,if it is infinite, then it is countably infinite. So, the set $\Bbb Q$ is …

Sep 26, 2021 · If a space is second-countable, the usual way to prove this will be to exhibit a specific countable basis. If a space is not second-countable, proving this can be more intricate, and what …

Mar 6, 2010 · A countable union of countable sets is countable. The proof would work because you can map the set N N to the countable union of countable sets, by mapping 1 1 to the first element of the …

My friend and I were discussing infinity and stuff about it and ran into some disagreements regarding countable and uncountable infinity. As far as I understand, the list of all natural numbers is

Feb 22, 2016 · I using the definition - If a set is countably infinite, then each element of the set can be mapped to the set of natural numbers. Another question - Is the cardinal product of countably infinite …

Apr 29, 2017 · We say $ { X }$ is Lindelöf if every open cover has a countable subcover. Th: Suppose $ { X }$ is second countable. Then it is Lindelöf. Pf: $ { X }$ admits a countable basis $ { \lbrace V _1, …

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