We describe the topology of systems $\{HD_{>γ} (x)\} _{γ∈Г}$ and $\{HD_{>γ}^c (x)\} _{γ∈Г}$ where $ HD_{>γ}(X)$ and $HD_{>γ}^c(X)$ are hyperspaces of compacta and subcontinua respectively of the Riemannian connected $n$ - dimensional compact manifold, the Hausdorff dimension of which is $ >γ; Г$ is some countable ordered subset in $[0; n), n ∈ \mathbb{N}$.

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