Conjugacy of Arbitrary n-Fold Mixing of Rohlin's Problem in Topological Sense

The Rohlin's problem is the leading problem in ergodic theory. This problem is closely related to harmonic analysis, probability theory, combinatorial number theory and so on. This paper mainly uses the topological conjugate with a special metric in topological dynamical system to study twofold mixing implies arbitrary n-fold mixing, where twofold mixing
$\mu(\mathrm{A}\cap \mathrm{T}^{-\mathrm{n}}\mathrm{B})\rightarrow\mu(\mathrm{A})\mu(\mathrm{B}), \mathrm{n}\in\mathrm{J}$
and
$\mathrm{n}\rightarrow\infty()$
[7]. From this we can obtain the recursive relation satisfying the special conditions. Thus twofold mixing implies arbitrary mixing for the order infinite system.