Dimensionsgrad for locally connected Polish spaces

Vitaly Fedorchuk; Jan van Mill

Fundamenta Mathematicae (2000)

  • Volume: 163, Issue: 1, page 77-82
  • ISSN: 0016-2736

Abstract

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

How to cite

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Fedorchuk, Vitaly, and van Mill, Jan. "Dimensionsgrad for locally connected Polish spaces." Fundamenta Mathematicae 163.1 (2000): 77-82. <http://eudml.org/doc/212430>.

@article{Fedorchuk2000,
abstract = {It is shown that for every n ≥ 2 there exists an n-dimensional locally connected Polish space with Dimensionsgrad 1.},
author = {Fedorchuk, Vitaly, van Mill, Jan},
journal = {Fundamenta Mathematicae},
keywords = {Dimensionsgrad; dimension; locally connected space; partition; cut; Polish space},
language = {eng},
number = {1},
pages = {77-82},
title = {Dimensionsgrad for locally connected Polish spaces},
url = {http://eudml.org/doc/212430},
volume = {163},
year = {2000},
}

TY - JOUR
AU - Fedorchuk, Vitaly
AU - van Mill, Jan
TI - Dimensionsgrad for locally connected Polish spaces
JO - Fundamenta Mathematicae
PY - 2000
VL - 163
IS - 1
SP - 77
EP - 82
AB - It is shown that for every n ≥ 2 there exists an n-dimensional locally connected Polish space with Dimensionsgrad 1.
LA - eng
KW - Dimensionsgrad; dimension; locally connected space; partition; cut; Polish space
UR - http://eudml.org/doc/212430
ER -

References

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  1. [1] P. S. Aleksandrov and B. A. Pasynkov, Introduction to Dimension Theory, Nauka, Moscow, 1973 (in Russian). 
  2. [2] L. E. J. Brouwer, Über den natürlichen Dimensionsbegriff, J. Reine Angew. Math. 142 (1913), 146-152. 
  3. [3] R. Engelking, General Topology, Heldermann, Berlin, 1989. 
  4. [4] R. Engelking, Theory of Dimensions: Finite and Infinite, Heldermann, Berlin, 1995. Zbl0872.54002
  5. [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. [6] V. V. Fedorchuk, Urysohn's identity and dimension of manifolds, Uspekhi Mat. Nauk 53 (1998), no. 5, 73-114 (in Russian). 
  7. [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). Zbl0995.54032
  8. [8] J. G. Hocking and G. S. Young, Topology, Addison-Wesley, Reading, Mass., 1961. 
  9. [9] W. Hurewicz and H. Wallman, Dimension Theory, Van Nostrand, Princeton, N.J., 1941. Zbl67.1092.03
  10. [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. Zbl0532.55001
  11. [11] K. Kuratowski, Topology I, II, PWN - Polish Scientific Publishers and Academic Press, Warszawa and New York, 1966. 
  12. [12] S. Mazurkiewicz, O arytmetyzacji continuów, C. R. Varsovie 6 (1913), 305-311. 
  13. [13] J. van Mill, Infinite-Dimensional Topology: Prerequisites and Introduction, North-Holland, Amsterdam, 1989. Zbl0663.57001
  14. [14] R. Pol, A weakly infinite-dimensional compactum which is not countable-dimen- sional, Proc. Amer. Math. Soc. 82 (1981), 634-636. Zbl0469.54014

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