In the mathematical field of topology a uniform isomorphism or uniform homeomorphism is a special isomorphism between uniform spaces that respects uniform properties.
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
If a uniform isomorphism exists between two uniform spaces they are called uniformly isomorphic or uniformly equivalent.
Examples
The uniform structures induced by equivalent norms on a vector space are uniformly isomorphic.
See also
- Homeomorphism—an isomorphism between topological spaces
- Isometric isomorphism—an isomorphism between metric spaces
References
- John L. Kelley, General topology, van Nostrand, 1955. P.181.