Abstract
By an invariant set in a metric space we mean a non-empty compact set K such that K = ⋃i=1nTi(K) for some contractions T1, …, Tn of the space. We prove that, under not too restrictive conditions, the union of finitely many invariant sets is an invariant set. Hence we establish collage theorems for non-affine invariant sets in terms of Lipschitzian retracts. We show that any rectifiable curve is an invariant set though there is a simple arc which is not an invariant set.
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