Variant of thin sets and their influence in 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 extended further if very thin sets are given to play main role instead of thin or finite sets which refines even statistical convergence. While developing the theory of very thin sets, concepts of super lacunary and very very thin sets are evolved spontaneously. Influence of very thin sets is reflected in various ways mainly in the BW property of the ideal consisting of very thin sets.