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Zero-dimensional CDH spaces with a dense completely metrizable subset

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Given a separable metrizable h-homogeneous space X, it is proved that X is a \(\textsf{CDH}\) space with a dense completely metrizable subspace if and only if every countable subset of… Click to show full abstract

Given a separable metrizable h-homogeneous space X, it is proved that X is a \(\textsf{CDH}\) space with a dense completely metrizable subspace if and only if every countable subset of X is included in a Polish subspace of X. We also show that every such space is \(\omega-\textsf{CDH}\).

Keywords: dimensional cdh; completely metrizable; zero dimensional; dense completely; subset

Journal Title: Acta Mathematica Hungarica
Year Published: 2019

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