A note on cohomological dimension of approximate movable spaces

We show that any approximate movable compact metric space X satisfies the equality $\dim X = {\dim _\mathbb{Z}}X$ without finite dimensional condition. Thus there is no approximate movable compact metric space X with $\dim X = \infty$ and ${\dim _\mathbb{Z}}X < \infty$. Since ANRs and some generalized ANRs are approximate movable, they satisfy the above equality.