Vol. 32, No. 1, 1970

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 329: 1
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Online Archive
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN: 1945-5844 (e-only)
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

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
Received: 3 April 1969
Published: 1 January 1970
Charles Harris Scanlon