Uniform topology

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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.

How to Cite This Entry:
Uniform topology. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article