Uniform isomorphism

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 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—an isomorphism between topological spaces
Isometric isomorphism—an isomorphism between metric spaces

References

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

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