# Uniform isomorphism

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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 ml|Equivalent_norms|Properties|equivalent norms on a vector space are uniformly isomorphic.

ee 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.

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