2023/05/25 by Paolo Leonetti, Leonetti, Paolo
Mathematics · Decision Sciences · #Approximation Theory and Sequence Spaces #Fuzzy and Soft Set Theory
paper · pdf · doi:10.48550/arxiv.2305.15928
We define the notion of ideal convergence for sequences (xn) with values in topological spaces X with respect to a family \Fη: η∈ X\ of subsets of X with η∈ Fη. Each set Fη quantifies the degree of accuracy of the convergence toward η. After proving that this is really a new notion, we provide some properties of the set of limit points and characterize the latter through the ideal cluster points and the ideal core of (xn).