In mathematics, a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence { x n } n = 1 ∞ {\displaystyle...

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...

of a separable Banach space need not be separable, but: Theorem — Let X {\displaystyle X} be a normed space. If X ′ {\displaystyle X'} is separable, then...

of space. From this perspective, the natural state space of a boson might seem to be a non-separable space. However, it is only a small separable subspace...

topology, a Polish space is a separable completely metrizable topological space; that is, a space homeomorphic to a complete metric space that has a countable...

higher than continuum). A separable measure space has a natural pseudometric that renders it separable as a pseudometric space. The distance between two...

mathematics, S-space is a regular topological space that is hereditarily separable but is not a Lindelöf space. L-space is a regular topological space that is...

roots is equal to its degree Separable sigma algebra, a separable space in measure theory Separable space, a topological space that contains a countable...

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

Fréchet–Urysohn space – Property of topological space Second-countable space – Topological space whose topology has a countable base Separable space – Topological...