2023/08/18 by Filipów, Rafał, Kwela, Adam
#03E17 (Primary) #03E35 (Secondary) #26A03 #40A30 #40A35 #54A20 #54C30 #FOS: Mathematics #General Topology (math.GN)
paper · doi:10.48550/arxiv.2308.09557
We examine topological spaces not distinguishing ideal pointwise and ideal σ-uniform convergence of sequences of real-valued continuous functions defined on them. For instance, we introduce a purely combinatorial cardinal characteristic (a sort of the bounding number \mathfrakb) and prove that it describes the minimal cardinality of topological spaces which distinguish ideal pointwise and ideal σ-uniform convergence. Moreover, we provide examples of topological spaces (focusing on subsets of reals) that do or do not distinguish the considered convergences. Since similar investigations for ideal quasi-normal convergence instead of ideal σ-uniform convergence have been performed in literature, we also study spaces not distinguishing ideal quasi-normal and ideal σ-uniform convergence of sequences of real-valued continuous functions defined on them.