2025/12/17 by Resteghini, Sirio, Straffelini, Cesare
Computer Science · Mathematics · #03E17 #54A25 (Primary) 54D10 #54D30 #54D55 (Secondary) #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #Optimization and Variational Analysis
paper · doi:10.48550/arxiv.2512.15593
openalex publication_date 2025/12/17 · openalex created_date 2025/12/19 · openalex updated_date 2026/07/28
A set of sequences is said to converge simultaneously if there exists an infinite subset H of the index set ω such that all sequences converge when restricted to H. We discuss simultaneous convergence of sequences in the same or in different sequentially compact spaces; we link the results for different spaces to ones for the same space; we show that simultaneous convergence happens for less than \mathfrak s sequences in spaces with weight bounded by \mathfrak s and for less than \mathfrak h sequences in general; we show a slight generalisation of these results in the context of Hausdorff spaces; and finally we investigate their optimality.