2020/04/28 by István Juhász, Juhász, István, Lajos Soukup +3
Decision Sciences · Mathematics · #54A25 #54A35 #Advanced Topology and Set Theory #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN)
paper · pdf · doi:10.48550/arxiv.2004.13423
openalex publication_date 2020/04/28 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
For a topological space X we propose to call a subset S ⊂ X "free in X" if it admits a well-ordering that turns it into a free sequence in X. The well-known cardinal function F(X) is then definable as sup\|S| : S is free in X\ and will be called the free set number of X. We prove several new inequalities involving F(X) and F(Xδ), where Xδ is the Gδ-modification of X: \bullet L(X) ≤ 2^2F(X) if X is T2 and L(X)≤ 2F(X) if X is T3; \bullet |X|≤ 2^2F(X) ⋅ ψc(X) ≤ 2^2F(X) ⋅ χ(X) for any T2-space X; \bullet F(Xδ)≤ 2^2^2F(X) if X is T2 and F(Xδ)≤ 2^2F(X) if X is T3.