On the existence of weakly 𝑛-dimensional spaces

van Mill, Jan; Pol, Roman

doi:10.1090/S0002-9939-1991-1056687-0

On the existence of weakly $n$-dimensional spaces
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by Jan van Mill and Roman Pol

Proc. Amer. Math. Soc. 113 (1991), 581-585

DOI: https://doi.org/10.1090/S0002-9939-1991-1056687-0

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Abstract:

Using a certain method for constructing peculiar large-dimensional spaces in every compactum with sufficiently large dimension, we present for every $n$ an easy example of a weakly $n$-dimensional space.

References

Ryszard Engelking, Teoria wymiaru, Biblioteka Matematyczna, Tom 51. [Mathematics Library, Vol. 51], Państwowe Wydawnictwo Naukowe, Warsaw, 1977 (Polish). MR 0482696
A. V. Ivanov, An example concerning Mazurkiewicz’ theorem, Seminar on General Topology, Moskov. Gos. Univ., Moscow, 1981, pp. 49–51 (Russian). MR 656948
Bronisław Knaster, Sur les coupures biconnexes des espaces euclidiens de dimension $n>1$ arbitraire, Rec. Math. [Mat. Sbornik] N.S. 19(61) (1946), 9–18 (Russian, with French summary). MR 0017520
J. Krasinkiewicz, Essential mappings onto products of manifolds, Geometric and algebraic topology, Banach Center Publ., vol. 18, PWN, Warsaw, 1986, pp. 377–406. MR 925878
J. Krasinkiewicz, Homotopy separators and mappings into cubes, Fund. Math. 131 (1988), no. 2, 149–154. MR 974664, DOI 10.4064/fm-131-2-149-154
John Kulesza, The dimension of products of complete separable metric spaces, Fund. Math. 135 (1990), no. 1, 49–54. MR 1074648, DOI 10.4064/fm-135-1-49-54

Topology

A. Lelek, Dimension inequalities for unions and mappings of separable metric spaces, Colloq. Math. 23 (1971), 69–91. MR 322829, DOI 10.4064/cm-23-1-69-91

Sur les problèmes

et

de Urysohn

10

Sur les ensembles de dimension faible

13

J. van Mill, Infinite-dimensional topology, North-Holland Mathematical Library, vol. 43, North-Holland Publishing Co., Amsterdam, 1989. Prerequisites and introduction. MR 977744
Jun-iti Nagata, Modern dimension theory, Revised edition, Sigma Series in Pure Mathematics, vol. 2, Heldermann Verlag, Berlin, 1983. MR 715431
Roman Pol, Countable-dimensional universal sets, Trans. Amer. Math. Soc. 297 (1986), no. 1, 255–268. MR 849478, DOI 10.1090/S0002-9947-1986-0849478-7
Leonard R. Rubin, R. M. Schori, and John J. Walsh, New dimension-theory techniques for constructing infinite-dimensional examples, General Topology Appl. 10 (1979), no. 1, 93–102. MR 519716, DOI 10.1016/0016-660x(79)90031-x

Sur les ensembles connexes et non connexes

2

B. Tomaszewski, On weakly $n$-dimensional spaces, Fund. Math. 103 (1979), no. 1, 1–8. MR 535830, DOI 10.4064/fm-103-1-1-8
A. V. Zarelua, Hereditarily infinite-dimensional spaces, Theory of sets and topology (in honour of Felix Hausdorff, 1868–1942), VEB Deutsch. Verlag Wissensch., Berlin, 1972, pp. 509–525 (Russian). MR 0343252