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## Fundamenta Mathematicae

1996 | 150 | 1 | 43-54
Tytuł artykułu

### The dimension of X^n where X is a separable metric space

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Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
For a separable metric space X, we consider possibilities for the sequence $S(X) = {d_n: n ∈ ℕ}$ where $d_n = dim X^n$. In Section 1, a general method for producing examples is given which can be used to realize many of the possible sequences. For example, there is $X_n$ such that $S(X_n) = {n, n+1, n+2,...}$, $Y_n$, for n >1, such that $S(Y_n) = {n, n+1, n+2, n+2, n+2,...}$, and Z such that S(Z) = {4, 4, 6, 6, 7, 8, 9,...}. In Section 2, a subset X of $ℝ^2$ is shown to exist which satisfies $1 = dim X = dim X^2$ and $dim X^3 = 2$.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
43-54
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-09-04
poprawiono
1995-11-17
Twórcy
autor
• George Mason University, Fairfax, Virginia, U.S.A.
Bibliografia
• [AK] R. D. Anderson and J. E. Keisler, An example in dimension theory, Proc. Amer. Math. Soc. 18 (1967), 709-713.
• [DRS] A. Dranishnikov, D. Repovš and E. Ščepin, On intersections of compacta of complementary dimensions in Euclidean space, Topology Appl. 38 (1991), 237-253.
• [E] R. Engelking, Dimension Theory, North-Holland, Amsterdam, 1978.
• [H] Y. Hattori, Dimension and products of topological groups, Yokohama Math. J. 42 (1994), 31-40.
• [K] J. Krasinkiewicz, Imbeddings into $ℝ^n$ and dimension of products, Fund. Math. 133 (1989), 247-253.
• [Ku1] J. Kulesza, Dimension and infinite products in separable metric spaces, Proc. Amer. Math. Soc. 110 (1990), 557-563.
• [Ku2] J. Kulesza, A counterexample to the extension of a product theorem in dimension theory to the noncompact case, preprint.
• [L] J. Luukkainen, Embeddings of n-dimensional locally compact metric spaces to 2n-manifolds, Math. Scand. 68 (1991), 193-209.
• [Sp] S. Spież, The structure of compacta satisfying dim(X × X) < 2 dim X, Fund. Math. 135 (1990), 127-145.
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Bibliografia
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