Journal of Convex Analysis 32 (2025), No. 4, 1083--1090
Copyright Heldermann Verlag 2025
Rough Families, Cluster Points, and Cores
Paolo Leonetti
Dept. of Economics, Università degli Studi dell'Insubria, Varese, Italy
leonetti.paolo@gmail.com
[Abstract-pdf]
We define the notion of ideal convergence for sequences $(x_n)$ with values in topological spaces $X$ with respect to a family $\{F_\eta: \eta \in X\}$ of subsets of $X$ with $\eta \in F_\eta$. Each set $F_\eta$ quantifies the degree of accuracy of the convergence toward $\eta$. 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 $(x_n)$.
Keywords: Rough convergence, rough family, ideal convergence, ideal core, ideal cluster points.
MSC: 40A35; 54A20.
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