Uniform isomorphism

In the mathematical field of topology a uniform isomorphism or uniform homeomorphism is a special isomorphism between uniform spaces that 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

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.

gollark: Hides it until it's not sick.
gollark: Automatically.
gollark: Er, basically, checking eggs to see if they're sick.
gollark: Either sickness checking, scraping, or view counting?
gollark: Ah, an email from dragcave. Apparently I have "by my own admission on the forums, done the exact same thing that got EATW banned from the API", whatever that was, oh well.

See also

  • Homeomorphism—an isomorphism between topological spaces
  • Isometric isomorphism—an isomorphism between metric spaces

References

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