Separable space information

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...

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...

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...

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

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...

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...

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...

in an n-dimensional Euclidean space. Then X 0 {\displaystyle X_{0}} and X 1 {\displaystyle X_{1}} are linearly separable if there exist n + 1 real numbers...

construction of Tsirelson space in 1974. The dual statement, that every separable Banach space is linearly isometric to a quotient space of ℓ1, was answered...

In quantum mechanics, separable states are multipartite quantum states that can be written as a convex combination of product states. Product states are...

p}(\Omega )} is a Banach space. For p < ∞ , W k , p ( Ω ) {\displaystyle p<\infty ,W^{k,p}(\Omega )} is also a separable space. It is conventional to denote...

topology, a cosmic space is any topological space that is a continuous image of some separable metric space. Equivalently (for regular T1 spaces but not in general)...

space is Polish if it is separable and completely metrizable, i.e. if it is homeomorphic to a separable and complete metric space. Polyadic A space is...

subset of this space, and this is a non-separable subset of the separable space S {\displaystyle \mathbb {S} } . It shows that separability does not inherit...

Any separable inner product space has an orthonormal basis. Using the Hausdorff maximal principle and the fact that in a complete inner product space orthogonal...

second-countable space is first countable, separable, and Lindelöf. Every σ-compact space is Lindelöf. Every metric space is first countable. For metric spaces, second-countability...

Marczewski proved that the topological dimension, for arbitrary metrisable separable space X, coincides with the Hausdorff dimension under one of the metrics...

a separable extension if for every α ∈ E {\displaystyle \alpha \in E} , the minimal polynomial of α {\displaystyle \alpha } over F is a separable polynomial...

separable spaces is a separable space and, thus, ccc. A metric space is ccc if and only if it's separable. In general, a ccc topological space need not...

space is a function whose composition with any element of the dual space is a measurable function in the usual (strong) sense. For separable spaces,...

separated if it is Hausdorff; importantly, "separated" does not mean separable. The topological and linear algebraic structures can be tied together...

on separable spaces and most applications to other areas of mathematics or physics only use separable Hilbert spaces. Note that if the measure spaces (X...

Arzelà–Ascoli theorem. A metric space is separable if and only if it is homeomorphic to a totally bounded metric space. The closure of a totally bounded...

For a stochastic process to be separable, in addition to other conditions, its index set must be a separable space, which means that the index set has...