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<p>The class of <i>L</i>Σ(≤ <i>ω</i>)-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 <i>L</i>Σ(≤ <i>ω</i>)-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 <i>L</i>Σ(≤ <i>ω</i>)-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 <i>L</i>Σ(≤ <i>ω</i>)-space. We also give insight to the structure of first-countable (<i>K</i>)<i>L</i>Σ(≤ <i>ω</i>)-compacta.</p>

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Some examples concerning LΣ(≤ ω) and metrizably fibered compacta

  • 期刊论文

  • 发表日期：

    2025年7月30日

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  • Antonio Avilés,
  • Mikołaj Krupski

摘要

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.