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

Kulesza, John. "The dimension of X^n where X is a separable metric space." Fundamenta Mathematicae 150.1 (1996): 43-54. <http://eudml.org/doc/212162>.

@article{Kulesza1996,
abstract = {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 $dim X^3 = 2$.},
author = {Kulesza, John},
journal = {Fundamenta Mathematicae},
keywords = {separable metric space},
language = {eng},
number = {1},
pages = {43-54},
title = {The dimension of X^n where X is a separable metric space},
url = {http://eudml.org/doc/212162},
volume = {150},
year = {1996},
}

TY - JOUR
AU - Kulesza, John
TI - The dimension of X^n where X is a separable metric space
JO - Fundamenta Mathematicae
PY - 1996
VL - 150
IS - 1
SP - 43
EP - 54
AB - 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 $dim X^3 = 2$.
LA - eng
KW - separable metric space
UR - http://eudml.org/doc/212162
ER -