Skip to main content Accessibility help
×
Home

0-dimensional compactifications and Boolean rings

  • K. D. Magill (a1) and J. A. Glasenapp (a2)

Extract

A subset of a topological space which is both closed and open is referred to as a clopen subset. Here, a 0-dimensional space is a Hausdorff space which has a basis of clopen sets. Here, a 0-dimensional space is a Hausdorff space which has a basis of clopen sets. By a compactification αX of a completely regular Hausdorff space X, we mean any compact space which contains X as a dense subspace. Two compactifications αX and γX are regarded as being equivalent if there exists a homeomorphism from αX onto γX which keeps X pointwise fixed. We will not distinguish between equivalent compactifications. With this convention, we can partially order any family of compactifications of X by defining αX ≧ γX if there exists a continuous mapping from γX onto αX which leaves X pointwise fixed. This paper is concerned with the study of the partially ordered family [X] of all 0-dimensional compactifications of a 0-dimensional space X.

    • 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.

      0-dimensional compactifications and Boolean rings
      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.

      0-dimensional compactifications and Boolean rings
      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.

      0-dimensional compactifications and Boolean rings
      Available formats
      ×

Copyright

References

Hide All
[1]Boboc, N. and Siretchi, Gh., ‘Sur la compactification d'un espace topologique’, Bull. Math. Sci. Math. Phys. R. P. Roumaine (N.S.) 5 (53) (1961), 155165 (1964).
[2]Gillman, L. and Jerison, M., Rings of continuous functions (D. Van Nostrand, New York, 1960).
[3]Lubben, R. G., ‘Concerning the decomposition and amalgamation of points, upper semi-continuous collections and topological extensions’, Trans. Amer. Math. Soc. 49 (1961), 410466
[4]Magill, K. D. Jr, ‘ A note on compactifications’, Math. Zeit. 94 (1966), 322325.
[5]Sierpinski, W., Introduction to general topology (The University of Toronto Press, 1934).
[6]Visliseni, J. and Flaksmaier, J., ‘The power and structure of the lattice of all compact extensions of a completely regular space’, Doklady 165, (1965), 14231425.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

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