IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-7091-6110-4_19.html
   My bibliography  Save this book chapter

Commentary on Menger’s “Untersuchungen über allgemeine Metrik”

In: Selecta Mathematica

Author

Listed:
  • Peter Plaumann
  • Karl Strambach

Abstract

The original models for topological spaces were subsets of the real line and its Cartesian powers, i.e., metric spaces. However, in the early years of the twentieth century, the founders of point-set topology strove to base that subject on concepts that were independent of any particular metric space notions and to expand the domain of validity of known metric space results to this more general setting. They also placed topological invariants into the foreground. It soon became apparent that many metric-space results retained their validity, but at a price — namely, the loss of geometric intuition and visualization; for example, there is no topological distinction between metric Spaces with equivalent metrics.

Suggested Citation

  • Peter Plaumann & Karl Strambach, 2002. "Commentary on Menger’s “Untersuchungen über allgemeine Metrik”," Springer Books, in: Bert Schweizer & Abe Sklar & Karl Sigmund & Peter Gruber & Edmund Hlawka & Ludwig Reich & Leopold Sc (ed.), Selecta Mathematica, pages 229-233, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7091-6110-4_19
    DOI: 10.1007/978-3-7091-6110-4_19
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-7091-6110-4_19. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.