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Inverse limit representations of hereditarily indecomposable compacta

Krasinkiewicz J.

Bulletin of the Polish Academy of Sciences. Mathematics

2003

Vol. 51, no 1

31-41

We prove that any infinite-dimensional hereditarily indecomposable compactum can be represented as the limit of an inverse sequence of compacta X0 <-- X1 <-- X2 <--..., where each Xk, k > O, is hereditarily indecomposable, dim Xk = k, and the bonding maps pk k+1 : X k+1 --> Xk are 1-dimensional monotone and surjective. Moreover, each bonding map pk k+l : Xk,l > 1, is l-dimensional. For finite dimensional hereditarily indecomposable compacta there exist analogous finite inverse sequences. Much the same results hold also for hereditarily unicoherent compacta.