Abstract

We define the notion of ideal convergence for sequences (xn)(x_n) with values in topological spaces XX with respect to a family {Fη:η∈X}\{F_\eta: \eta \in X\} of subsets of XX with η∈Fη\eta \in F_\eta. Each set FηF_\eta quantifies the degree of accuracy of the convergence toward η\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 (xn)(x_n).

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Keywords

  • Rough convergence
  • rough family
  • ideal convergence
  • ideal core
  • ideal cluster points

Mathematics Subject Classification

40A35; 54A20

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Suggested citation

P. Leonetti. “Rough Families, Cluster Points, and Cores.” Journal of Convex Analysis 32 (2025), No. 4, 1083–1090. https://doi.org/10.68381/jca32057

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Published by Heldermann Verlag, 2025. Rights now held by Banach Press.