Vol. 84, No. 2, 1979

Recent Issues
Vol. 325: 1
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Vol. 319: 1  2
Vol. 318: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
Quasicompactifications and shape theory

Billy Joe Ball

Vol. 84 (1979), No. 2, 251–259
Abstract

If f : X Y is an embedding of a space X into a space Y such that each component of Y is a compactification of the image of a quasicomponent of X and such that f induces a homeomorphism of the space QX of quasicomponents of X onto the space of components of Y , then (f,Y ) is called a quasicompactification of X. After some preliminary results, it is shown that a locally compact metric space X has a locally compact metric quasicompactiflcation if and only if QX is locally compact. Two canonical quasicompactifications, FX and αX, of such a space are described, and it is shown that if ShpX = ShpY , then ShpFX = ShpFY ; the question whether also ShpαX = ShpαY is left open. Finally, some techniques of this paper are used to obtain a proper shape version of a theorem due to Y. Kodama, generalizing previous work of the author.

Mathematical Subject Classification 2000
Primary: 54B15
Secondary: 54C56
Milestones
Received: 30 January 1979
Published: 1 October 1979
Authors
Billy Joe Ball