Year: 2026
Type: preprint
Abstract: We continue the study of ideal convergence for sequences $(x_n)$ with values in a topological space $X$ with respect to a family $\{F_η:η\in X\}$ of subsets of $X$ with $η\in F_η$, 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.
Source: arXiv (Cornell University)
Author: Leonetti, Paolo
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7125196777
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