Raising dimension under all projections

• Autorzy: John Cobb
• Języki publikacji: EN

Abstrakty

EN

As a special case of the general question - "What information can be obtained about the dimension of a subset of $ℝ^n$ by looking at its orthogonal projections into hyperplanes?" - we construct a Cantor set in $ℝ^3$ each of whose projections into 2-planes is 1-dimensional. We also consider projections of Cantor sets in $ℝ^n$ whose images contain open sets, expanding on a result of Borsuk.

Kategorie tematyczne

• 54F45: Dimension theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1994
• Tom: 144
• Numer: 2
• Strony: 119-128

Daty

wydano

1994

otrzymano

1992-07-02

poprawiono

1993-06-02

Twórcy

autor

John Cobb

• Mathematics Department, University of Idaho, Moscow, Idaho 83843, U.S.A.

Bibliografia

• [B] K. Borsuk, An example of a simple arc in space whose projection in every plane has interior points, Fund. Math. 34 (1947), 272-277.
• [E] R. Engelking, Dimension Theory, PWN, Warszawa, and North-Holland, Amsterdam, 1978.
• [M] S. Mardešić, Compact subsets of $R^n$ and dimension of their projections, Proc. Amer. Math. Soc. 41 (2) (1973), 631-633.
• [R] Referee's comment