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<p>The set <i>dd</i>(<i>X</i>) of densities of all dense subspaces of a topological space <i>X</i> is called the double density spectrum of <i>X</i>. In this note we present a couple of results that imply <i>λ</i> ∈ <i>dd</i>(<i>X</i>), provided that <i>X</i> is a <i>compact</i> Hausdorff space and <i>λ</i> is a cardinal satisfying certain conditions.</p><p>As a consequence of these, we prove that <i>dd</i>(<i>X</i>) = [<i>d</i>(<i>X</i>), <i>w</i>(<i>X</i>)] holds for any polyadic space <i>X</i>. This, in turn, implies that <i>dd</i>(<i>G</i>) = [<i>d</i>(<i>G</i>), <i>w</i>(<i>G</i>)] for any locally compact topological group <i>G</i>.</p>

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On the double density spectra of compact spaces

  • 期刊论文

  • 发表日期：

    2025年1月20日

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  • István Juhász,
  • Jan van Mill

摘要

The set dd(X) of densities of all dense subspaces of a topological space X is called the double density spectrum of X. In this note we present a couple of results that imply λ ∈ dd(X), provided that X is a compact Hausdorff space and λ is a cardinal satisfying certain conditions.

As a consequence of these, we prove that dd(X) = [d(X), w(X)] holds for any polyadic space X. This, in turn, implies that dd(G) = [d(G), w(G)] for any locally compact topological group G.