In the mathematical field of topology a uniform isomorphism or uniform homeomorphism is a special isomorphism between uniform spaces that respects uniform properties. Uniform spaces with uniform maps form a category. An isomorphism between uniform spaces is called a uniform isomorphism.
A function between two uniform spaces and is called a uniform isomorphism if it satisfies the following properties
If a uniform isomorphism exists between two uniform spaces they are called uniformly isomorphic or uniformly equivalent.
A uniform embedding is an injective uniformly continuous map between uniform spaces whose inverse is also uniformly continuous, where the image has the subspace uniformity inherited from
The uniform structures induced by equivalent norms on a vector space are uniformly isomorphic.