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.
Read more about this topic: Uniform Isomorphism
Famous quotes containing the word definition:
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)