topological vector space

Most of the above hold for other topological vector spaces X too.

At this time he was a leading expert in the theory of topological vector spaces.

This definition usually appears in the context of topological vector spaces.

Every relatively compact set in a topological vector space is bounded.

In such topological vector spaces one can consider series of vectors.

Köthe's best known work has been in the theory of topological vector spaces.

Every topological vector space has a local base of absorbing and balanced sets.

Any topological vector space over a connected field is connected.

The articles on the various flavours of topological vector spaces go into more detail about these.

A hyperplane on a topological vector space X is either dense or closed.

This turns the dual into a locally convex topological vector space.

Let E be a separable, real, topological vector space.

Below are some common topological vector spaces, roughly ordered by their niceness.

In functional analysis, it sometimes refers to a polar topology on a topological vector space.

Schauder bases can also be defined analogously in a general topological vector space.

These functions form a complete topological vector space with a suitably defined family of seminorms.

Let be a topological vector space, denote the interior operator, and then:

Sequence spaces are typically equipped with a norm, or at least the structure of a topological vector space.

On every infinite-dimensional topological vector space there is a discontinuous linear map.

They are the most commonly used topological vector spaces, and their topology comes from a norm (mathematics).

Hence, every topological vector space is an abelian topological group.

F-spaces are complete topological vector spaces with a translation-invariant metric.

The topological vector space is called "initial object" or "initial structure" with respect to the given data.

From a conceptual point of view, all notions related to topological vector spaces should match the topology.

There do exist generalizations when V is an infinite dimensional topological vector space.