Talk:Oscillation (mathematics)

From Wikipedia, the free encyclopedia

Why is it that for 1/x the oscillation is undefined at -∞ and +∞. I would naively think it is zero.67.171.64.190 09:27, 4 June 2007 (UTC)

You are correct. I noticed the same thing. Oleg Alexandrov (talk) 15:28, 4 June 2007 (UTC)

[edit] Another notion of oscillation

There is also another notion -- oscillation of a function (say from a topological space to a metric space) defined by

\inf\{d(f(U)); U\text{ is an open neighborhood of }x\}.

(It is commonly used that the set of points of discontinuity is a Gδ set.) Do we have this notion defined in some other article on wiki? If not, perhaps an article oscillation of a function could be started. --Kompik 10:47, 7 October 2007 (UTC)

(Of course, d(A) in the above definition stands for diameter of a set A.) --Kompik 11:10, 7 October 2007 (UTC)