Influence of different kind of thin sets in the theory of convergence

Abstract

A class of subsets designated as very thin subsets of natural numbers has been studied and seen that theory of convergence may be rediscovered if very thin sets are given to play main role instead of thin or finite sets which removes some drawback of statistical convergence. While developing the theory of very thin sets, concepts of super thin, very very thin and super super thin sets are evolved spontaneously.