It is proved that the sequence of continuum hyperspaces in $\mathbb{I}^n$  with Hausdorff dimension $> α_i$ constructs $\mathcal{F}_σ$ -absorbing sequence in  $\exp^c (\mathbb{I}^n)$  for arbitrary sequence $(α_i), 1 < α_1 < α_2 < ... < n$.

[1] K.J.Falkoner The Geometry of Fractal Sets. - Cambridge University Press,1985.

[2] T. Banakh, T. Radul, M. Zarichnyi Absorbing Sets in Infinite-Dimensional Manifolds. - VNTL Publishers, 1996.

[3] J. Baars, H. Gladdines, J. van Mill Absorbing systems in infinite-dimensional manifolds // Topology Appl. - 1993. - Vol. 50. - B2. - P.147-182.

[4] H. Gladdines and J. van Mill Absorbing systems in infinite-dimensional manifolds and applications. - Amsterdam, Vrije Universiteit, 1994.

[5] R. Cauty Suites $\mathcal{F}_σ$-absorbantes en theorie de la dimension // Fundamenta Mathematicae. - 1999. - Vol. 159. - B2. P.115-126.

[6] N. Mazurenko Absorbing sets related to Hausdorff dimension // Visn. Lviv. Univ.

[7] M.M. Zarechny Topology of functors and monads in the category of compact sets. - Kyiv, ISDO, 1993.

[8] J. van Mill . The Infinite-Dimensional Topology of Function Spaces. - Amsterdam: Elsevier, 2001. - Vol.64. - 630 p.