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

Kulesza, John

Kulesza, John

Fundamenta Mathematicae, Tome 149 (1996), p. 43-54 / Harvested from The Polish Digital Mathematics Library

Résumé

For a separable metric space X, we consider possibilities for the sequence $S (X) = d_{n} : n \in ℕ$ where $d_{n} = d i m X^{n}$ . 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 $1 = d i m X = d i m X^{2}$ and $d i m X^{3} = 2$ .

Publié le : 1996-01-01

Zbl 0870.54034

EUDML-ID : urn:eudml:doc:212162

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     author = {John Kulesza},
     title = {The dimension of X^n where X is a separable metric space},
     journal = {Fundamenta Mathematicae},
     volume = {149},
     year = {1996},
     pages = {43-54},
     zbl = {0870.54034},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv150i1p43bwm}
}

Kulesza, John. The dimension of X^n where X is a separable metric space. Fundamenta Mathematicae, Tome 149 (1996) pp. 43-54. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv150i1p43bwm/

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