For any ergodic transformation $T$ of the Lebesgue space $(X,\mu)$ it is possible to introduce the topology $\tau$ into $X$ such that a) with provided topology $X$ becomes the totally disconnected compact (Cantor set) with the structure of a Markov compact and $\mu$ becomes a Borel Markov measure. b) $T$ becomes a minimal strictly ergodic homeomorphism of $(X,\tau)$; c) orbit partition of $T$ is the tail partition of the Markov compact upto two classes of the partition. The structure of Markov compact is the same as a structure of the pathes in the Bratteli diagram of some $AF$-algebra. Bibliography: 19 titles.