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Dense metrizable subspaces in powers of Corson compacta

Arkady Leiderman, Santi Spadaro, Stevo Todorcevic

Abstract

We characterize when the countable power of a Corson compactum has a dense metrizable subspace and construct consistent examples of Corson compacta whose countable power does not have a dense metrizable subspace. We also give several remarks about ccc Corson compacta and, as a byproduct, we obtain a new proof of Kunen and van Mill's characterization of when a Corson compactum supporting a strictly positive measure is metrizable.

Dense metrizable subspaces in powers of Corson compacta

Abstract

We characterize when the countable power of a Corson compactum has a dense metrizable subspace and construct consistent examples of Corson compacta whose countable power does not have a dense metrizable subspace. We also give several remarks about ccc Corson compacta and, as a byproduct, we obtain a new proof of Kunen and van Mill's characterization of when a Corson compactum supporting a strictly positive measure is metrizable.
Paper Structure (5 sections, 16 theorems, 10 equations)

This paper contains 5 sections, 16 theorems, 10 equations.

Table of Contents

  1. Introduction
  2. Powers of Corson compact spaces
  3. Corson compacta with the countable chain condition
  4. Corson compacta and singular cardinals
  5. Concluding remarks

Key Result

Lemma 1

A Corson compactum has a dense metrizable subspace if and only if it has a $\sigma$-disjoint $\pi$-base.

Theorems & Definitions (27)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Corollary 1
  • proof
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • ...and 17 more