Each nowhere dense nonvoid closed set in Rn is a σ-limit set

Volume 149 / 1996

Andrei G. Sivak Fundamenta Mathematicae 149 (1996), 183-190 DOI: 10.4064/fm-149-2-183-190


We discuss main properties of the dynamics on minimal attraction centers (σ-limit sets) of single trajectories for continuous maps of a compact metric space into itself. We prove that each nowhere dense nonvoid closed set in $ℝ^n$, n ≥ 1, is a σ-limit set for some continuous map.


  • Andrei G. Sivak

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