The topology generated by a uniform structure. In more detail, let be a set equipped with a uniform structure (that is, a uniform space) , and for each let denote the set of subsets of as runs through the entourages of . Then there is in one, and moreover only one, topology (called the uniform topology) for which is the neighbourhood filter at for any . A topology is called uniformizable if there is a uniform structure that generates it. Not every topological space is uniformizable; for example, non-regular spaces.
For references see Uniform space.
Uniform topology. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Uniform_topology&oldid=16188