Vol. 44, No. 2, 1973

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
On Hausdorff compactifications

Marlon C. Rayburn

Vol. 44 (1973), No. 2, 707–714
Abstract

Given a pair of spaces X and Y , a necessary and sufficient condition is found for Y to be homeomorphic to cl αX(αX X) for some compactification αX of X. From this follows a necessary and sufficient condition for Y to be homeomorphic to αX X for some αX. As an application, a sufficient condition is found to insure the isomorphism of the upper semi-lattices of compactifications K(X) and K(Y ) for arbitrary X and Y , and in consequence it appears that for every space X, there is a pseudocompact space Y with K(X) isomorphic to K(Y ). A necessary condition for K(X) to be isomorphic to K(Y ) is observed for arbitrary X and Y , and this leads to the consideration of spaces compactly generated at infinity. Examples are constructed.

Mathematical Subject Classification 2000
Primary: 54D35
Secondary: 54D50
Milestones
Received: 30 September 1971
Revised: 27 September 1972
Published: 1 February 1973
Authors
Marlon C. Rayburn