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2 Bulletin of the Polish Academy of Sciences. Mathematics

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Group structures and rectifiability in powers of spaces

Ridderbos G. J.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

Vol. 55, no 4

357-363

We prove that if some power of a space X is rectiflable, then X[sup]πω(x) is rectifiable. It follows that no power of the Sorgenfrey line is a topological group and this answers a question of Arhangeliskiî. We also show that in Mal'tsev spaces of point-countable type, character and π-character coincide.

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.