Vol. 101, No. 2, 1982

Download this article
Download this article. For screen
For printing
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
Extending functions from products with a metric factor and absolutes

Teodor C. Przymusiński

Vol. 101 (1982), No. 2, 463–475
Abstract

Extendability of continuous functions from products with a metric or a paracompact p-space factor is studied. We introduce and investigate completions mX and pX of a completely regular space X defined as “largest” spaces Y containing X as a dense subspace such that every continuous real-valued function extends continuously from X × Z over Y × Z where Z is a metric or a paracompact p-space, respectively. We study the relationship between mX (resp. pX) and the Hewitt realcompactification vX (resp. the Dieudonné completion μX) of X. We show that for normal and countably paracompact spaces mX = vX and pX = μX, but neither normality nor countable paracompactness alone suffices. The relationship between completions mX and pX and the absolute EX of X is discussed.

Mathematical Subject Classification 2000
Primary: 54C20
Secondary: 54B10, 54D35
Milestones
Received: 21 May 1980
Revised: 20 February 1981
Published: 1 August 1982
Authors
Teodor C. Przymusiński