• Corpus ID: 239016650

The Covering Dimension of the Sorgenfrey Plane

@inproceedings{Sipacheva2021TheCD,
  title={The Covering Dimension of the Sorgenfrey Plane},
  author={Ol'ga Sipacheva},
  year={2021}
}
It is proved that the square of the Sorgenfrey line has infinite covering dimension. Covering dimension dim was originally introduced by Lebesgue for domains in Euclidean spaces [1]. In 1933 Čech extended Lebesgue’s definition to completely regular spaces [2], and in 1950 Katětov proposed a different definition, which coincided with Čech’s one for normal spaces [3]. Since then, these two versions of covering dimension have become equally popular. Thus, the books [4], [5], and [6] use Čech’s… 

References

SHOWING 1-10 OF 11 REFERENCES
Dimension Theory of General Spaces
1. Topological spaces, normality and compactness 2. Paracompact and pseudo- metrizable spaces 3. Covering dimension 4. Inductive dimension 5. Local dimension 6. Images of zero-dimensional spaces 7.
The dimension of product spaces.
  • M. L. Wage
  • Mathematics, Medicine
    Proceedings of the National Academy of Sciences of the United States of America
  • 1978
TLDR
A separable metric space X and a paracompact space Y are constructed such that dim X + dim Y = 0 < 1 = dim(X x Y).
Dimension Theory: A Selection of Theorems and Counterexamples
Topology (Academic, London, 1966), Vol. 1. Department of General Topology and Geometry, Faculty of Mechanics and Mathematics, M
  • 1999
On the zero-dimensionality of some non-normal product spaces
  • Sci. Rep. Tokyo Kyoiku Daigaku, Sect. A 11 (296), 167–174 (1972).
  • 1972
Dimension Theory (Academic
  • New York,
  • 1970
A theorem on the Lebesgue dimension
Příspěvek k theorii dimense
  • Časopis Pěst. Mat. Fys
  • 1933
Př́ıspěvek k theorii dimense
  • Časopis Pěst. Mat. Fys. 62, 277–291 (1933). 4 OL’GA SIPACHEVA
  • 1933
Sur une décomposition d’un intervalle en une infinité non dénombrable d’ensembles non mesurables
  • C. R. Acad. Sci. Paris 165, 422–424 (1917).
  • 1917
...
1
2
...