Uniform topology
From Encyclopedia of Mathematics
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.
Comments
For references see Uniform space.
How to Cite This Entry:
Uniform topology. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Uniform_topology&oldid=32017
Uniform topology. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Uniform_topology&oldid=32017
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article