Uniform isomorphism

In the mathematical field of topology a uniform isomorphism or uniform homeomorphism is a special isomorphism between uniform spaces which respects uniform properties.

Definition

A function f between two uniform spaces X and Y is called a uniform isomorphism if it satisfies the following properties

• f is a bijection
• f is uniformly continuous
• the inverse function f ^-1 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 is an isomorphism between topological spaces
• isometric isomorphism is an isomorphism between metric spaces

References

• John L. Kelley, General topology, van Nostrand, 1955. P.181.