# 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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