On finite-dimensional maps and other maps with "small" fibers

• Autorzy: Yaki Sternfeld
• Języki publikacji: EN

Abstrakty

EN

We prove that if f is a k-dimensional map on a compact metrizable space X then there exists a σ-compact (k-1)-dimensional subset A of X such that f|X∖A is 1-dimensional. Equivalently, there exists a map g of X in $I^k$ such that dim(f × g)=1. These are extensions of theorems by Toruńczyk and Pasynkov obtained under the additional assumption that f(X) is finite-dimensional.
 These results are then extended to maps with fibers restricted to some classes of spaces other than the class of k-dimensional spaces. For example: if f has weakly infinite-dimensional fibers then dim(f|X∖A) ≤ 1 for some σ-compact weakly infinite-dimensional subset A of X. The proof applies essentially the properties of hereditarily indecomposable continua.

Kategorie tematyczne

• 54F15: Continua and generalizations
• 54F45: Dimension theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1995
• Tom: 147
• Numer: 2
• Strony: 127-133

Daty

wydano

1995

otrzymano

1994-08-29

poprawiono

1994-12-12

Twórcy

autor

Yaki Sternfeld

• Department of Mathematics, University of Haifa, Haifa 31905, Israel

Bibliografia

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• [D-R] T. Dobrowolski and L. Rubin, The hyperspaces of infinite dimensional compacta for covering and cohomological dimension are homeomorphic, Pacific J. Math. 104 (1994), 15-39.
• [K] K. Kuratowski, Topology II, PWN, Warszawa, 1968.
• [Le] M. Levin, A short construction of hereditarily infinite dimensional compacta, Topology Appl., to appear.
• [Pa] B. A. Pasynkov, On dimension and geometry of mappings, Dokl. Akad. Nauk SSSR 221 (1975), 543-546 (in Russian).
• [Po] R. Pol, On light mappings without perfect fibers on compacta, preprint.
• [T] H. Toruńczyk, Finite to one restrictions of continuous functions, Fund. Math. 75 (1985), 237-249.