Vol. 32, No. 1, 1970

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Vol. 297: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Some continuity properties of the Schnirelmann density. II

R. L. Duncan

Vol. 32 (1970), No. 1, 65–67
Abstract

Let S denote the set of all infinite increasing sequences of positive integers. For all A{an} and B = {bn} in S define the metric ρ(A,B) = 0 if A = B; i.e., if an = bn for all n and ρ(A,B) = 1∕k otherwise, where k is the smallest value of n for which anbn. The main object of this note is to show that the set of points of continuity of the Schnirelmann density d(A) is a residual set and that this is the best possible result of this type.

Mathematical Subject Classification
Primary: 10.63
Milestones
Received: 6 February 1968
Revised: 15 July 1969
Published: 1 January 1970
Authors
R. L. Duncan