Abstract
By the decomposition theorem dim X ≦ n if and only if X admits a decomposition into n+1 zero-dimensional subspaces Z i for i = 0,... n. If f: X → X is a homeomorphism, then under some dimensional restrictions on the set of periodic points, the Z i can be chosen to be images of Z 0 under iterates of f.
Similar content being viewed by others
References
J. M. Aarts and T. Nishiura, Dimension and Extension, North-Holland (Amsterdam, 1991).
R. Engelking, Theory of Dimensions, Finite and Infinite, Sigma Series in Pure Mathematics 10 (Lemgo, 1995).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Aarts, J.M., Fokkink, R.J. & Vermeer, J. A dynamical decomposition theorem. Acta Math Hung 94, 191–196 (2002). https://doi.org/10.1007/s10474-002-0002-7
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10474-002-0002-7