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For a dynamical system {St} on a metric space X, we examine the question whether the topological properties of X are inherited by the global attractor A (if it exists). When {St} is jointly continuous, we prove that the Čech-Alexander-Spanier cohomology groups of A are isomorphic to the corresponding cohomology groups of X. The same conclusion is obtained in the case where {St} is a group and A has a bounded neighborhood which is a deformation retract of X. © 1999 Elsevier Science B.V.




Gobbino, M. (2001). Topological properties of attractors for dynamical systems. Topology, 40(2), 279–298. https://doi.org/10.1016/S0040-9383(99)00061-0

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