The topological entropy of a continuous map 
on a compact
space 
measures the exponential growth of distinguishable orbit segments using finite open covers. For a finite open
cover 
,
let 
be the smallest number of its members that cover 
, and define the join 
. Then
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
where the supremum is taken over finite open covers 
of 
(Adler et al. 1965). Unlike Kolmogorov entropy,
this definition does not require an invariant probability
measure.
