Vol. 44, No. 2, 1973

Download this article
Download this article. For screen
For printing
Recent Issues
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
Vol. 324: 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
A topological lemma and applications to real functions

Clifford Edward Weil

Vol. 44 (1973), No. 2, 757–765
Abstract

In working with functions of Baire class one having the Darboux property, one of the most useful tools has been a theorem due to Baire that says a function of Baire class one has a point of continuity on every closed set relative to the closed set. The lemma mentioned in the title can be used in many instances more efficiently than Baire’s theorem as is shown in §4. It is concerned with sets rather than functions and hence more basic than Baire’s Theorem, and easier to prove requiring only one application of Baire’s category theorem.

Mathematical Subject Classification 2000
Primary: 26A21
Secondary: 26A15, 26A69
Milestones
Received: 10 August 1971
Published: 1 February 1973
Authors
Clifford Edward Weil