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 gage space as each seminorm induces a pseudometric.

See also: Gauge space, Family (mathematics), If and only if, Locally convex space, Mathematics, Metric space, Pseudometric, Seminorm, Topological space