Vol. 33, No. 3, 1970

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 305: 1
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
On the equivalence of normality and compactness in hyperspaces

James Edgar Keesling

Vol. 33 (1970), No. 3, 657–667
Abstract

Let X be a topological space and 2X the space of all closed subsets of X with the finite topology. Assaming the continuum hypothesis it is shown that 2X is normal if and only if X is compact. It is not known if the continuum hypothesis is a necessary assumption, but it is shown that for X a k-space, 2X normal implies X compact. A theorem about the compactification of the n-th symmetric product of a space X is first proved which then plays an important part in the proof of the above results.

Mathematical Subject Classification
Primary: 54.20
Milestones
Received: 26 September 1969
Revised: 5 December 1969
Published: 1 June 1970
Authors
James Edgar Keesling