Sentence examples for a normed structure from inspiring English sources

By an orthogonality normed space we mean an orthogonality space having a normed structure.

In this paper we show that normed structures which can be axiomatized in positive bounded logic (in the sense of Henson and Iovino) admit proof-theoretic metatheorems (as developed by the second author since 2005) on the extractability of explicit uniform bounds from proofs in the respective theories.

After observing the investigations of this paper, we can comment that while studyingthe n-normed structure, the main issue should be the use of the meaning ofn-norms.

For some relevant works on 2-normed structure and its extension to n (≥2 -normed structure and subsequent applications, one may refer to [14–30].

By an orthogonality normed space (normed module) we mean an orthogonality space (resp., module) having a normed (resp., normed module) structure.

Let be a normed space with norm.

Let be a normed vector space with norm.

Let Y denote a normed space with the norm | ⋅ |.

(A nonempty convex subset of a normed linear space is said to have normal structure if each bounded convex subset of consisting of more than one point contains a nondiametral point).

Let X be a normed vector space with the norm ∥ ⋅ ∥.

If is a normed space with as its convex subset, then is a convex structure in consequently (1.3) and (1.4), respectively, become.