Porosity Supremum-Infimum and Porosity Convergence

Abstract

In this paper, by using porosity notion for subsets of natural numbers at infinity porosity lower and porosity upper bound of real valued sequences will be defined. By using these new notions, definitions of porosity infimum and porosity supremum will be given, respectively. For a given sequence, the equivalence of porosity infimum and porosity supremum is necessary and sufficient condition for to existence of porosity convergence but it is necessary, not sufficient, condition for to existence of usual convergence.