Mean dimension of a compact metrizable dynamical system measures the covering dimension required
per orbit coordinate. For a homeomorphism 
, it is
 |
where 
ranges over finite open covers and 
is the least order of an open refinement. The order is
one less than the largest number of members with a nonempty common intersection,
and 
is the common refinement by intersections. The limit exists by subadditivity. Finite-dimensional compact systems have mean dimension zero,
while the supremum may be infinite for an infinite-dimensional
space.
Minimality means that every orbit is dense.
