2020/04/18 by Jorge Antonio Cruz Chapital, Chapital, Jorge Antonio Cruz
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.2004.08496
openalex publication_date 2020/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (X,τ) be a Hausdorff space and n∈ω. We prove that if X admits a continuous selection over Fn(X) (nonempty subsets of X of cardinality at most n), then for every n≤ m≤ 2n such that m is not a prime number, X admits a continuous selection over [X]m (subsets of X of cardinality m). As a consequence of this, a space X admits a continuous selection for every natural number if and only if the same is true for every prime number. For Hausdorff spaces (X,τ) which admit continuous selections over [X]2, we characterize the existence of continuous selections over [X]n for n≥ 2, in terms of a covering-type property.