nLab weak topology of a topological vector space

Idea

The weak topology on a topological vector space $(V, \tau)$ is the initial topology induced by its linear functionals $V \longrightarrow \mathbb{R}$ that are continuous with respect to its originally given topology $\tau$.

Beware that in other contexts the term “weak topology” (see there) is used for other initial topologies.

References

See also:

• Wikipedia: The weak and weak-star topologies