Oscillation

Noun

1. the act of oscillating or the state of being oscillated
2. a regular periodic fluctuation in value about some mean
3. a single such cycle
4. defined for each point x {\displaystyle x} in the domain of the function by inf { d i a m ( f ( U ) ) ∣<!-- ∣ --> U i s a n e i g h b o r h o o d o f x } {\displaystyle \inf \left\{\mathrm {diam} (f(U))\mid U\mathrm {\ is\ a\ neighborhood\ of\ } x\right\}} , and describes the difference (possibly ∞) between the limit superior and limit inferior of the function near that point.