Uniform spaces

Uniform continuity

Uniform spaces with uniform maps form a category. An isomorphism between uniform spaces is called a uniform isomorphism; explicitly, it is a uniformly continuousbijection whose inverse is also uniformly continuous. A uniform embedding is an injective uniformly continuous map ${\displaystyle i:X\to Y}$ between uniform spaces whose inverse ${\displaystyle i^{-1}:i(X)\to X}$ is also uniformly continuous, where the image ${\displaystyle i(X)}$ has the subspace uniformity inherited from ${\displaystyle Y.}$