second countable

Adjective

Meaning

second countable (not comparable)

Alternative form of second-countable

second-countable (not comparable)

(topology) Such that its topology has a countable base, said of a topological space.

Source: en.wiktionary.org

Alternative names

second-countable

Examples

Every second-countable space is first-countable, separable, and Lindelöf. Source: Internet

For example, a compact Hausdorff space is metrizable if and only if it is second-countable. Source: Internet

Urysohn's Theorem can be restated as: A topological space is separable and metrizable if and only if it is regular, Hausdorff and second-countable. Source: Internet

; Second-countable : A space is second-countable or perfectly separable if it has a countable base for its topology. Source: Internet

Separability versus second countability Any second-countable space is separable: if is a countable base, choosing any from the non-empty gives a countable dense subset. Source: Internet

What Urysohn had shown, in a paper published posthumously in 1925, was that every second-countable normal Hausdorff space is metrizable). Source: Internet

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