Gauge space

In topology and related areas of mathematics a gauge space is a topological space where the topology is defined by a family of pseudometrics.

A space is uniformizable if and only if it is a gauge space.

Examples

• A metric space is trivially a gauge space as the topology is given by one metric.
• A locally convex space, where the topology is given by a family of seminorms, is a gauge space as each seminorm induces a pseudometric.