Vol. 84, No. 2, 1979

Recent Issues
Vol. 332: 1  2
Vol. 331: 1  2
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
Ultra-Hausdorff H-closed extensions

Jack Ray Porter and R. Grant Woods

Vol. 84 (1979), No. 2, 399–411
Abstract

Introduction. A Hausdorff topological space X is called ultra-Hausdorff if, given two distinct points p and q of X, there is an open-and-closed (henceforth called “clopen”) subset A of X such that p A and qA. A Hausdorff space X is H-closed if, whenever it is embedded as a subspace of another Hausdorff space Y , it is a closed subset of Y . In this paper we characterize those Hausdorff spaces that have ultra-Hausdorff H-closed extensions and construct, for such spaces, the projective maximum of the set of ultra-Hausdorff H-closed extensions. We compare this projective maximum to the Katětov H-closed extension, and examine when continuous functions can be continuously extended to this projective maximum.

Mathematical Subject Classification 2000
Primary: 54D35
Secondary: 54D15
Milestones
Received: 16 October 1978
Published: 1 October 1979
Authors
Jack Ray Porter
R. Grant Woods