Vol. 32, No. 1, 1970

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
Rings of functions with certain Lipschitz properties

Charles Harris Scanlon

Vol. 32 (1970), No. 1, 197–201
Abstract

Let (X, d) denote a metric space, Le(X) the ring of real valued functions on X which are Lipschitz on each compact subset of X,L1(X) the ring of real valued functions on X which are locally Lipschitz relative to the completion of X, and Lc(X),L1(X) the bounded elements of Lc(X),L1(X). The relations between equality of these rings and the topological properties of X are studied. It is shown that a subspace (S,d) of (X, d) is Lc-embedded (or Lc-embedded) in (X, d) if and only if S is closed. Further, every subspace of (X, d) is L1 and L1-embedded in (X,d).

Mathematical Subject Classification
Primary: 46.55
Milestones
Received: 3 April 1969
Published: 1 January 1970
Authors
Charles Harris Scanlon