Some continuity properties of the Schnirelmann density. II

R. L. Duncan

Vol. 32 (1970), No. 1, 65–67

DOI: 10.2140/pjm.1970.32.65

Abstract

Let S denote the set of all infinite increasing sequences of positive integers. For all A≅{a_n} and B = {b_n} in S define the metric ρ(A,B) = 0 if A = B; i.e., if a_n = b_n for all n and ρ(A,B) = 1∕k otherwise, where k is the smallest value of n for which a_n≠b_n. 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