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.

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.

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

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

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

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

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

Instead one needs to define Lie groups modeled on more general locally convex topological vector spaces.

Some generalizations to Banach spaces and more general topological vector spaces are possible.

When dealing with topological vector spaces, the definition is made instead for elements , the continuous dual space.

This left adjoint defines "free topological vector spaces".

FK-spaces are examples of topological vector spaces.

When dealing with topological vector spaces, one is typically only interested in the continuous linear functionals from the space into the base field.

This generalisation also applies to topological vector spaces and, more generally, to uniform spaces.

It can be called a principled theory, based on duality theory for topological vector spaces.

Many topological vector spaces are locally convex.

However, there are topological vector spaces whose topology is not induced by a norm but are still of interest in analysis.

The closed graph theorem can be generalized to more abstract topological vector spaces in the following way:

The Gâteaux derivative extends the concept to locally convex topological vector spaces.

Continuous linear mappings between topological vector spaces preserve boundedness.

Further, for topological vector spaces, one can define a continuous dual space, and in this case a dual basis may exist.

Topological vector spaces are vector spaces with a compatible topology.

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.