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Second-countable space
Topological space whose topology has a countable base
Second-countable space
In topology, a second-countable space, also called a completely separable space, is a topological space whose topology has a countable base. More explicitly, a topological space T {\displaystyle T} is second-countable if there exists some countable collection U = { U i } i = 1 ∞ {\displaystyle {\mathcal {U}}=\{U_{i}\}_{i=1}^{\infty }} of open subsets of T {\displaystyle T} such that any open subset of T {\displaystyle T} can be written as a union of elements of some subfamily of U {\displaystyle...
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