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A note on indecomposability of chaotic continua on surfaces

Kato H.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

Vol. 46, no 1

11-16

In [5, 6] and [8], we proved that if a plane compactum X with dim X > 0 admits a continuum-wise expansive homeomorphism f, then X is not locally connected and it contains a sigma-chaotic continuum Z (sigma = s or u) of f such that Z is indecomposable and for each z [...] Z, the continuum-wise sigma-stable set V[sup sigma] (z, Z) coincides with the composant containing z. In this note, we generalize this theorem to 1-dimensional compacta in arbitrary surfaces.