A function is topologically transitive if, given any two intervals and , there is some positive integer such that . Vaguely, this means that neighborhoods of points eventually get flung out to "big" sets so that they don't necessarily stick together in one localized clump.

# Topologically Transitive

## See also

Chaos## Explore with Wolfram|Alpha

## Cite this as:

Weisstein, Eric W. "Topologically Transitive."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/TopologicallyTransitive.html