Skip to main content

The Countable Sum Theorem for Covering Dimension

  • Chapter
  • First Online:
Dimension Theory

Part of the book series: Atlantis Studies in Mathematics ((ATLANTISSM,volume 7))

  • 697 Accesses

Abstract

In this chapter we prove two of the most important results for covering dimension, the countable sum theorem for normal spaces and the subset theorem for perfectly normal spaces. Both results are due to Čech.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 59.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    For a proof see [48, 108] or [92].

References

  1. E. Čech, Contribution to the theory of dimension, Časopis Pěst. Mat. Fys. 62, 277–291 (1933) (in Czech); English transl.: [84, pp. 149–160]

  2. S. Eilenberg, E. Otto, Quelques propriétés caractéristiques de la dimension. Fund. Math. 31, 149–153 (1938)

    Article  Google Scholar 

  3. R. Engelking, General Topology (Heldermann Verlag, Berlin, 1989)

    MATH  Google Scholar 

  4. E. Hemmingsen, Some theorems in dimension theory for normal Hausdorff spaces. Duke Math. J. 13, 495–504 (1946)

    Article  MathSciNet  Google Scholar 

  5. W. Kulpa, The Poincaré–Miranda theorem. Amer. Math. Monthly 104, 545–550 (1997)

    MathSciNet  MATH  Google Scholar 

  6. J. van Mill, The Infinite–Dimensional Topology of Function Spaces (Elsevier, Amsterdam, 2001)

    MATH  Google Scholar 

  7. K. Morita, On the dimension of normal spaces. I. Japan. J. Math. 20, 5–36 (1950)

    Article  MathSciNet  Google Scholar 

  8. N.B. Vedenisoff, On dimension in the sense of Čech. Izv. Akad. Nauk Ser. Mat. 5, 211–216 (1941) (in Russian)

    Google Scholar 

  9. H. Wallman, Lattices and topological spaces. Ann. Math. 39, 112–126 (1938)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Charalambous, M.G. (2019). The Countable Sum Theorem for Covering Dimension. In: Dimension Theory. Atlantis Studies in Mathematics, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-030-22232-1_3

Download citation

Publish with us

Policies and ethics