In the mathematical field of topology a uniform isomorphism or 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.
Definition
A function between two uniform spaces and is called a uniform isomorphism if it satisfies the following properties
is a bijection is uniformly continuous the inverse function is uniformly continuous
In other words, a uniform isomorphism is a uniformly continuous bijection between uniform spaces whose inverse is also uniformly continuous.
If a uniform isomorphism exists between two uniform spaces they are called or .
Uniform embeddings
A is an injective uniformly continuous map between uniform spaces whose inverse is also uniformly continuous, where the image has the subspace uniformity inherited from
Examples
The uniform structures induced by equivalent norms on a vector space are uniformly isomorphic.
See also
— an isomorphism between topological spaces — an isomorphism between metric spaces
References
, pp. 180-4