Skip to main content Accessibility help
×
Home

Hausdorff Compactifications as Epireflections

  • W. N. Hunsaker (a1) and S. A. Naimpally (a2)

Abstract

We answer the following problem posed by Herrlich in the affirmative: “Can the Freudenthal compactification be regarded as a reflection in a sensible way?” This is accomplished by exploiting the one-to-one correspondence between proximities compatible with a given Tihonov space and compactifications of that space. We give topological characterizations of proximally continuous functions for the proximities associated with the Freudenthal and Fan-Gottesman compactifications.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Hausdorff Compactifications as Epireflections
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Hausdorff Compactifications as Epireflections
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Hausdorff Compactifications as Epireflections
      Available formats
      ×

Copyright

References

Hide All
1. Dickman, R. F. Jr, Some characterizations of the Freudenthal compactification of a semicompact space, Proc. Amer. Math. Soc. 19 (1968), 631633.
2. Fan, K. and Gottesman, N., On compactifications of Freudenthal and Wallman, Indag. Math. 14 (1952), 504510.
3. Freudenthal, H., Kompaktisierungen und Bikompaktisierungen, Indag. Math. 13 (1951) 184192.
4. Herrlich, H., Categorical Topology, General Topology and Applications 1 (1971), 115.
5. Morita, K., On bicompactifications of semibicompact spaces, Sci. Rep. Tokyo Bunrika Daigaku Sect. A 4 (1952), 222229.
6. Naimpally, S. A. and Warrack, B. D., Proximity Spaces, Cambridge Tract in Mathematics and Mathematical Physics No. 59, Cambridge University Press (1970).
7. Smirnov, Y. M., On proximity spaces, Math. Sb. 31 (73) (1952), 543–574; English translation in Amer. Math. Soc. Transi. (2) 38 (1964), 5–36.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Keywords

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed