Sentence examples for separable spaces from inspiring English sources

This extends the result by J. Bourgain and G. Pisier in (1983) [6] for separable spaces.

However, both definitions are identical for separable spaces which do not contain.

This embedding property is satisfied by a very general class of Banach spaces, for instance subspaces of a space with Markushevich basis, as WCG spaces (and so separable and reflexive spaces), dual of separable spaces as, and so forth.

The classical theorem states that the inverse of an injective bounded linear mapping between Banach spaces is continuous; but Ishihara (1994), working with separable spaces, has shown that the best possible conclusion in BISH is the sequential continuity of the inverse map, and that to pass from that to full continuity, it is necessary and sufficient to work in BISH + BD-N.

We also give a formula for the Szlenk power type of the E-direct sum of separable spaces provided that E has a shrinking unconditional basis whose dual basis yields an asymptotic ℓp structure in E⁎.

The method produces, among others, the only separable Banach space of almost-universal disposition with respect to the class F of finite-dimensional spaces (Gurariĭ space G); or the only, under CH, Banach space with density character the continuum which is of universal disposition with respect to the class S of separable spaces (Kubis space K).

If X is a separable space, then (X widehat{F})) is also a separable space.

If is a real separable space such that either.

Let X be a separable space and S an equicontinuous set in X γ,U).

We also showed that a separable space such that has and is sequentially compact has the.

Let X be a separable space, A a closed subset of X and (varphi colonOmegatimes Xmultimap X) a measurable map with nonempty closed values.