Science Fair Project Encyclopedia
Uniform isomorphism
(Redirected from Uniformly homeomorphic)
In the mathematical field of topology a uniform isomorphism or uniform homeomorphism is a special isomorphism between uniform spaces which respects uniform properties.
Definition
A function f between two uniform spaces X and Y is called 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.
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
10-26-2009 08:16:03
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details