Physical Sciences and Mathematics Commons^™

Some Properties Of Certain Sets Of Coprime Integers, Roger C. Entringer

Mathematics & Statistics ETDs

The set P(n) of all primes equal to or less than n has the obvious property that it contains exactly one multiple of each prime equal to or less than n. We use this partial description of P(n) as a basis for the following

Definition 1.1. An increasing sequence {a₁,...,a_k} of integers greater than 1 is a coprime chain if it contains exactly one multiple of each prime equal to or less than a_k.

Convergence Functions And Their Related Topologies, Darrell C. Kent

Mathematics & Statistics ETDs

A convergence function is a correspondence between the filters on a given set S and the subsets of S which specifies which filters converge to which points of S. This concept is defined to include types of convergence which are more general than that defined by specifying a topology on S. Thus a convergence function may be regarded as a generalization of a topology.