generalization of a uniformity
for every ,
for every , there is such that ,
where is defined as the inverse relation (http://planetmath.org/OperationsOnRelations) of , and is the composition of relations (http://planetmath.org/OperationsOnRelations). If satisfies Axiom 1, then is called a semi-uniformity. If satisfies Axiom 2, then is called a quasi-uniformity. The underlying set equipped with is called a semi-uniform space or a quasi-uniform space according to whether is a semi-uniformity or a quasi-uniformity.
A semi-pseudometric space is a semi-uniform space. A quasi-pseudometric space is a quasi-uniform space.
- 1 W. Page, Topological Uniform Structures, Wiley, New York 1978.
|Title||generalization of a uniformity|
|Date of creation||2013-03-22 16:43:09|
|Last modified on||2013-03-22 16:43:09|
|Last modified by||CWoo (3771)|