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

Fundamenta Mathematicae (1996)

- Volume: 150, Issue: 1, page 43-54
- ISSN: 0016-2736

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topKulesza, 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 -

## References

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