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In the mathematical field of topology a **uniform isomorphism** or **uniform homeomorphism** is a special isomorphism between uniform spaces that respects uniform properties. Uniform spaces with uniform maps form a category. An isomorphism between uniform spaces is called a uniform isomorphism.

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

- is a bijection
- is uniformly continuous
- the inverse function is uniformly continuous

In other words, a **uniform isomorphism** is a uniformly continuous bijection between uniform spaces whose inverse is also uniformly continuous.

If a uniform isomorphism exists between two uniform spaces they are called **uniformly isomorphic** or **uniformly equivalent**.

**Uniform embeddings**

A ** uniform embedding** is an injective uniformly continuous map between uniform spaces whose inverse is also uniformly continuous, where the image has the subspace uniformity inherited from

The uniform structures induced by equivalent norms on a vector space are uniformly isomorphic.

- Homeomorphism – Mapping which preserves all topological properties of a given space — an isomorphism between topological spaces
- Isometric isomorphism – Distance-preserving mathematical transformation — an isomorphism between metric spaces

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