Uniform isomorphism

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

Definition[edit]

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

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

Examples[edit]

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

See also[edit]

References[edit]