a normed vector space

In functional analysis, a Banach space is a normed vector space that allows vector length to be computed.

a vector space with a metric that allows the computation of vector length and distance between vecto

Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vecto ...

a complete normed vector space such that every Cauchy sequence (with respect to the metric d(x, y) = |x - y|) in B has a limit in B.

A Banach space, B, is a complete normed vector space such that every Cauchy sequence (with respect to the metric d(x, y) = |x - y|) in B has a limit in B.

a closed linear subspace of the space of bounded sequences,

a Banach space is a closed linear subspace of the space of bounded sequences, ℓ∞, and contains as a closed subspace the Banach space c0 of sequences converging to zero.

A space which is complete under the metric induced by a norm

A space which is complete under the metric induced by a norm is a Banach space.

the name for complete normed vector spaces, one of the central objects of study in functional analysis

In mathematics, Banach spaces is the name for complete normed vector spaces, one of the central objects of study in functional analysis.