Dimensionsgrad for locally connected Polish spaces

• Autorzy: Vitaly V. Fedorchuk , Jan van Mill
• Języki publikacji: EN

Abstrakty

EN

It is shown that for every n ≥ 2 there exists an n-dimensional locally connected Polish space with Dimensionsgrad 1.

Słowa kluczowe

EN

Dimensionsgrad; dimension; locally connected space

Kategorie tematyczne

• 55M10: Dimension theory
• 54F45: Dimension theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2000
• Tom: 163
• Numer: 1
• Strony: 77-82

Daty

wydano

2000

otrzymano

1999-05-12

poprawiono

1999-10-05

Twórcy

autor

Vitaly V. Fedorchuk

• Chair of General Topology and Geometry, Mech. Math. Faculty, Moscow State University, 119-899 Moscow, Russia

autor

Jan van Mill

• Faculteit der Exacte Wetenschappen, Divisie Wiskunde en Informatica, Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, the Netherlands

Bibliografia

• [1] P. S. Aleksandrov and B. A. Pasynkov, Introduction to Dimension Theory, Nauka, Moscow, 1973 (in Russian).
• [2] L. E. J. Brouwer, Über den natürlichen Dimensionsbegriff, J. Reine Angew. Math. 142 (1913), 146-152.
• [3] R. Engelking, General Topology, Heldermann, Berlin, 1989.
• [4] R. Engelking, Theory of Dimensions: Finite and Infinite, Heldermann, Berlin, 1995.
• [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.
• [6] V. V. Fedorchuk, Urysohn's identity and dimension of manifolds, Uspekhi Mat. Nauk 53 (1998), no. 5, 73-114 (in Russian).
• [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).
• [8] J. G. Hocking and G. S. Young, Topology, Addison-Wesley, Reading, Mass., 1961.
• [9] W. Hurewicz and H. Wallman, Dimension Theory, Van Nostrand, Princeton, N.J., 1941.
• [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.
• [11] K. Kuratowski, Topology I, II, PWN - Polish Scientific Publishers and Academic Press, Warszawa and New York, 1966.
• [12] S. Mazurkiewicz, O arytmetyzacji continuów, C. R. Varsovie 6 (1913), 305-311.
• [13] J. van Mill, Infinite-Dimensional Topology: Prerequisites and Introduction, North-Holland, Amsterdam, 1989.
• [14] R. Pol, A weakly infinite-dimensional compactum which is not countable-dimen- sional, Proc. Amer. Math. Soc. 82 (1981), 634-636.