Uniformly homeomorphic - Definition and Overview

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 uniform isomorphism if it satisfies the following properties

• f is a bijection
• f is uniformly continuous
• the inverse function f ^-1 is uniformly continuous

See also

• homeomorphism is an isomorphism between topological spaces