2023/07/11 by Antonio Avilés, Avilés, Antonio, Mikołaj Krupski +1
Mathematics · #26A21 54F05 #54C60 #54D30 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2307.05271
openalex publication_date 2023/07/11 · openalex created_date 2023/07/13 · openalex updated_date 2026/07/28
The class of LΣ(≤ω)-spaces was introduced in 2006 by Kubiś, Okunev and Szeptycki as a natural refinement of the classical and important notion of Lindelöf Σ-spaces. Compact LΣ(≤ω)-spaces were considered earlier, under different names, in the works of Tkachuk and Tkachenko in relation to metrizably fibered compacta. In this paper we give counterexamples to several open questions about compact LΣ(≤ω)-spaces that are scattered in the literature. Among other things, we refute a conjecture of Kubiś, Okunev and Szeptycki by constructing a separable Rosenthal compactum which is not an LΣ(≤ω)-space. We also give insight to the structure of first-countable (K)LΣ(≤ω)-compacta.