# normed space

## normed space

(mathematics)
A vector space with a function, ||F||, such that

||F|| = 0 if and only if F=0 ||aF|| = abs(a) * ||F|| ||F+G|| <= ||F|| + ||G||

Roughly, a distance between two elements in the space is defined.
References in periodicals archive ?
In [1] Baker proved that every isometry from a normed space into a strictly convex normed linear space is affine.
Let X be a normed space, let D be a convex subset of X, and let c > 0.
h(gI) is a normed space with the norm [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
By an orthogonality normed space, we mean an orthogonality space having a normed structure.
Let (X, q) be a semi normed space over the field C of complex numbers with the semi norm q.
To show that a normed space is a Hilbert space, we prove that the normed spaces comes from an inner product.
Kaiser in (14) proved the stability of monomial functional equation where the functions map a normed space over a field with valuation to a Banach space over a field with valuation and the control function is of the form [epsilon]([||x||.
The concept of a linear 2-normed space was introduced as a natural 2-metric analogue of that of a normed space.
Many problems for partial difference and integro-difference equations can be written as difference equations in a normed space.
A subspace of a normed space is a closed linear manifold; the closure [M.
Let E be a normed space, U an open subset of E and G, F [member of] [A.
There exists a non-complete real normed space whose totally antiproximinal convex subsets are not rare.

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