Uniform isomorphism

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 . 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 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 The uniform structures induced by equivalent norms on a vector space are uniformly isomorphic.