It is shown that for every n ≥ 2 there exists an n-dimensional locally connected Polish space with Dimensionsgrad 1.
@article{bwmeta1.element.bwnjournal-article-fmv163i1p77bwm, author = {Vitaly Fedorchuk and Jan van Mill}, title = {Dimensionsgrad for locally connected Polish spaces}, journal = {Fundamenta Mathematicae}, volume = {163}, year = {2000}, pages = {77-82}, zbl = {0944.54025}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv163i1p77bwm} }
Fedorchuk, Vitaly; van Mill, Jan. Dimensionsgrad for locally connected Polish spaces. Fundamenta Mathematicae, Tome 163 (2000) pp. 77-82. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv163i1p77bwm/
[00000] [1] P. S. Aleksandrov and B. A. Pasynkov, Introduction to Dimension Theory, Nauka, Moscow, 1973 (in Russian).
[00001] [2] L. E. J. Brouwer, Über den natürlichen Dimensionsbegriff, J. Reine Angew. Math. 142 (1913), 146-152.
[00002] [3] R. Engelking, General Topology, Heldermann, Berlin, 1989.
[00003] [4] R. Engelking, Theory of Dimensions: Finite and Infinite, Heldermann, Berlin, 1995. | Zbl 0872.54002
[00004] [5] V. V. Fedorchuk, The fundamentals of dimension theory, in: Encyclopedia Math. Sci. 17, A. V. Arkhangel'skiĭ and L. S. Pontryagin (eds.), Springer, Berlin, 1990, 91-202.
[00005] [6] V. V. Fedorchuk, Urysohn's identity and dimension of manifolds, Uspekhi Mat. Nauk 53 (1998), no. 5, 73-114 (in Russian).
[00006] [7] V. V. Fedorchuk, M. Levin and E. V. Shchepin, On Brouwer's definition of dimension, ibid. 54 (1999), no. 2, 193-194 (in Russian). | Zbl 0995.54032
[00007] [8] J. G. Hocking and G. S. Young, Topology, Addison-Wesley, Reading, Mass., 1961.
[00008] [9] W. Hurewicz and H. Wallman, Dimension Theory, Van Nostrand, Princeton, N.J., 1941. | Zbl 67.1092.03
[00009] [10] D. M. Johnson, The problem of the invariance of dimension in the growth of modern topology, Part II, Arch. Hist. Exact Sci. 25 (1981), 85-267. | Zbl 0532.55001
[00010] [11] K. Kuratowski, Topology I, II, PWN - Polish Scientific Publishers and Academic Press, Warszawa and New York, 1966.
[00011] [12] S. Mazurkiewicz, O arytmetyzacji continuów, C. R. Varsovie 6 (1913), 305-311.
[00012] [13] J. van Mill, Infinite-Dimensional Topology: Prerequisites and Introduction, North-Holland, Amsterdam, 1989. | Zbl 0663.57001
[00013] [14] R. Pol, A weakly infinite-dimensional compactum which is not countable-dimen- sional, Proc. Amer. Math. Soc. 82 (1981), 634-636. | Zbl 0469.54014