The sets of are called entourages or vicinities. The set together with the uniform structure is called a uniform space.
If is an entourage, then for any we say that and are -close.
Every uniform space can be considered a topological space with a natural topology induced by uniform structure. The uniformity, however, provides in general a richer structure, which formalize the concept of relative closeness: in a uniform space we can say that is close to as is to , which makes no sense in a topological space. It follows that uniform spaces are the most natural environment for uniformly continuous functions and Cauchy sequences, in which these concepts are naturally involved.
|Date of creation||2013-03-22 12:46:26|
|Last modified on||2013-03-22 12:46:26|
|Last modified by||mps (409)|