## Stream: new members

### Topic: uniformity

#### Kenny Lau (Oct 21 2018 at 17:28):

Let's say s is an open set. Is { p | p.1 in s iff p.2 in s } in the uniformity?

#### Kenny Lau (Oct 21 2018 at 17:29):

what would be the set in the uniformity associated to this open set?

#### Kenny Lau (Oct 21 2018 at 17:29):

or is that the wrong thing to ask?

#### Sebastien Gouezel (Oct 21 2018 at 19:01):

Elements of the uniformity are uniform neighborhoods of the diagonal. The set you write is not a neighborhood of the diagonal, so it can not belong to the uniformity. In general, there is no element of the uniformity canonically associated to an open set, as the uniformity is really a global notion. In a topological group, however, if s is a neighborhood of the identity, then {p | p.1 - p.2 \in s} belongs to the uniformity.

Last updated: May 10 2021 at 18:22 UTC