On rough ideal convergence

2026/01/20 by Paolo Leonetti · 1 voice
Mathematics · #math.GN #math.CA #math.FA

paper · pdf

Abstract

We continue the study of ideal convergence for sequences (x_n) with values in a topological space X with respect to a family \F_η:η∈ X\ of subsets of X with η∈ F_η, where each F_η measures the allowed ``roughness'' of convergence toward η. More precisely, after introducing the corresponding notions of cluster and limit points, we prove several inclusion and invariance properties, discuss their structural properties, and give examples showing that the rough notions are genuinely different from the classical ideal ones.

Citations

• On generalized limits and ultrafilters
• The Category Dichotomy for Ideals
• Borel complexity of sets of ideal limit points
• Rough families, cluster points, and cores
• The Borel complexity of ideal limit points
• Regular matrices of unbounded linear operators
• Analytic P-ideals and Banach spaces
• On the Relationship between Ideal Cluster Points and Ideal Limit Points
• On the relationship between ideal cluster points and ideal limit points
• Characterizations of Ideal Cluster Points
• Representations of ideals in Polish groups and in Banach spaces

Discussions

• Paolo Leonetti: On rough ideal convergence https://arxiv.org/abs/2601.13805 https://arxiv.org/pdf/2601.13805 https://arxiv.org/html/2601.13805 [bsky, 0 points, 0 comments]

Related

• Rough families, cluster points, and cores
• Rough ideal convergence in a partial metric space
• Rough Weighted Ideal Convergence and Korovkin-Type Approximation via weighted equi-ideal convergence
• Thinnable Ideals and Invariance of Cluster Points
• Characterizations of Ideal Cluster Points