In the mathematical field of topology a uniform isomorphism or uniform homeomorphism is a special isomorphism between uniform spaces which respects uniform properties.
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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 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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