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
- 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.
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
- John L. Kelley, General topology, van Nostrand, 1955. P.181.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.