Inverse limit representations of hereditarily indecomposable compacta

• Autorzy: Krasinkiewicz J.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

dimension; hereditarily indecomposable compacta; inverse sequences; monotone mappings; products

PL

wymiar; ciąg odwrotny; odwzorowanie monotoniczne; iloczyn

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2003
• Tom: Vol. 51, no 1
• Strony: 31--41
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Krasinkiewicz J.

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland,

Bibliografia

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• [3] J. Krasinkiewicz, Essential mappings onto products of manifolds, in: Geometric and algebraic topology, Banach Center Publications, 18, PWN, Warszawa (1986) 377-406.
• [4] K. K. Kuratowski, Topology, vol. II, PWN, Warszawa; Academic Press, New York and London 1968.
• [5] L. G. Oversteegen, E. D. Tymchatyn, On hereditarily indecomposable compacta, in: Geometric and algebraic topology, Banach Center Publications, 18, PWN, Warszawa (1986) 407-417.
• [6] R. Pol, A 2-dimensional compactum in the product of two 1-dimensional compacta which does not contain any rectangle, Topology Proc., 16 (1991) 133-135.