2016/12/20 by István Juhász, Juhász, István, Lajos Soukup +3
Computer Science · Mathematics · #54A25 #54D20 #54D55 #Advanced Banach Space Theory #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN)
paper · pdf · doi:10.48550/arxiv.1612.06651
openalex publication_date 2016/12/20 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
A topological space X is called almost discretely Lindelöf if every discrete set D ⊂ X is included in a Lindelöf subspace of X. We say that the space X is \em μ-sequential if for every non-closed set A ⊂ X there is a sequence of length ≤ μ in A that converges to a point which is not in A. With the help of a technical theorem that involves elementary submodels, we establish the following two results concerning such spaces. (1) For every almost discretely Lindelöf T3 space X we have |X| ≤ 2χ(X). (2) If X is a μ-sequential T2 space of pseudocharacter ψ(X) ≤ 2μ and for every free set D ⊂ X we have L(D) ≤ μ, then |X| ≤ 2μ. The case χ(X) = ω of (1) provides a solution to Problem 4.5 from "I. Juhász, V. Tkachuk, and R. Wilson, Weakly linearly Lindelöf monotonically normal spaces are Lindelöf", while the case μ= ω of (2) is a partial improvement on the main result of "A.V. Archangel'skii and R.Z. Buzyakova, On some properties of linearly Lindelöf spaces".