2019/06/01 by T. Banakh, Banakh, T., S. Bardyla +3
Computer Science · Mathematics · #54B30 #54D30 #54D35 #54D80 #Advanced Algebra and Logic #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN)
paper · pdf · doi:10.48550/arxiv.1906.00185
openalex publication_date 2019/06/01 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
Let κ be an infinite cardinal. A topological space X is κ-bounded if the closure of any subset of cardinality ≤κ in X is compact. We discuss the problem of embeddability of topological spaces into Hausdorff (Urysohn, regular) κ-bounded spaces, and present a canonical construction of such an embedding. Also we construct a (consistent) example of a sequentially compact separable regular space that cannot be embedded into a Hausdorff ω-bounded space.