- Uniform isomorphism
In the mathematical field of

topology a**uniform isomorphism**or**uniform homeomorphism**is a specialisomorphism betweenuniform 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" isuniformly continuous

* theinverse function "f"^{ -1}is uniformly continuousIf 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 betweentopological spaces

*isometric isomorphism is an isomorphism betweenmetric spaces **References***

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

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