IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4612-6290-9_3.html
   My bibliography  Save this book chapter

Compactness

In: Counterexamples in Topology

Author

Listed:
  • Lynn Arthur Steen

    (Saint Olaf College)

  • J. Arthur Seebach Jr.

    (Saint Olaf College)

Abstract

A space satisfies a certain separation axiom only if the topology contains enough open sets to provide disjoint neighborhoods for certain disjoint sets. Compactness, however, limits the number of open sets in a topology, for every open cover of a compact topological space must contain a finite sub-cover. This difference between the separation axioms and the various forms of compactness is illustrated in the extreme by the double pointed finite complement topology (Example 18.7) which is not even T0 yet does satisfy all the forms of compactness.

Suggested Citation

  • Lynn Arthur Steen & J. Arthur Seebach Jr., 1978. "Compactness," Springer Books, in: Counterexamples in Topology, edition 0, chapter 0, pages 18-27, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-6290-9_3
    DOI: 10.1007/978-1-4612-6290-9_3
    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:978-1-4612-6290-9_3. 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.