IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-94-017-0141-9_4.html

Topological Spaces

In: Functional Analysis

Author

Listed:
  • Erdoğan S. Şuhubi

    (Yeditepe University, Department of Mathematics)

Abstract

While we were discussing, in the preceding chapter, some fundamental concepts associated with real analysis we observed that concepts such as convergence, limit, continuity of functions, compactness or denseness can be properly defined and effectively exploited by employing certain subsets of the set of real numbers with appropriate properties which we have called open sets that are essentially unions of open intervals. In this chapter, inspired by that approach, we try to extend some concepts developed in real analysis to an arbitrary set X through an appropriately chosen class of its subsets enabling us to introduce a kind of notion of “nearness” between objects in this set. This class then defines a topology on X. Sets equipped with topologies will be called topological spaces. We shall briefly discuss here their structures and various properties sufficiently to meet our demands in the future chapters.

Suggested Citation

  • Erdoğan S. Şuhubi, 2003. "Topological Spaces," Springer Books, in: Functional Analysis, chapter 0, pages 221-260, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-0141-9_4
    DOI: 10.1007/978-94-017-0141-9_4
    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

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:978-94-017-0141-9_4. 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.