Pringsheim convergence of double sequences for uniform boundedness principle

摘要

The set of all pairs of positive integers is considered as a directed set under the direction: (m,n) ≤ (i,j) if and only if m ≤ i and n ≤ j. This directed set is used for Pringsheim-type convergence of double sequences. Consequences of uniform boundedness principle through double sequences are derived in this paper.