Talk:Neighbourhood
From Maths
These two definitions (and some others) are equivalent in the following sense: they give different bases of the same filter. By others I mean, in a metric space, just open balls (or closed balls, with positive radius). And in a product of topological spaces, a product of neighborhoods (only finitely many being nontrivial). Etc.
A good practice is, to use neighborhoods only in such phrase: "...for all points of some neighborhood of x..." In this case, the choice of a base does not matter.
Sometimes one writes "open neighborhood" when needed. Boris (talk) 20:12, 23 March 2016 (UTC)
