2023/12/31 by Pedro Emerick, Emerick, Pedro, Luan Arjuna Belmonte +1
Mathematics · #15A03 #46A16 #46B87 #46J30 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2401.00382
openalex publication_date 2023/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we investigate the concept of infinite dense-lineability recently introduced by M. Calderón-Moreno, P. Gerlach-Mena and J. Prado-Bassas. We answer a question posed by the authors about the equivalence between infinite (pointwise) dense-lineability and (pointwise) dense-lineability. We prove that the equivalence always holds in first-countable topological vector spaces and under some assumptions about the weight of the topology. However, the equivalence is not always true, as shown in an example. Furthermore, we introduce the notions of infinite (α,β)-dense-lineability and infinite (strongly) dense-algebrability and obtain some analogous results in these cases. We also obtain a criterion for strongly dense-algebrability for sets of the form X∖ Y, where X is a free algebra and Y is a free subalgebra of X.