On dimensional properties of infinite-dimensional spaces
Smirnov, Yu.
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Displaying similar documents to “Countable-dimensional spaces: a survey”
On dimensional properties of infinite-dimensional spaces
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Concerning infinite-dimensional spaces
Tumarkin, L.
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Countable dense homogeneity and λ-sets
Rodrigo Hernández-Gutiérrez, Michael Hrušák, Jan van Mill (2014)
Fundamenta Mathematicae
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We show that all sufficiently nice λ-sets are countable dense homogeneous (𝖢𝖣𝖧). From this fact we conclude that for every uncountable cardinal κ ≤ 𝔟 there is a countable dense homogeneous metric space of size κ. Moreover, the existence of a meager in itself countable dense homogeneous metric space of size κ is equivalent to the existence of a λ-set of size κ. On the other hand, it is consistent with the continuum arbitrarily large that every 𝖢𝖣𝖧 metric space has size either ω₁...
Countable dense homogeneous spaces
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A. A. Fora (1981)
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Fundamenta Mathematicae
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We construct in ZFC a cosmic space that, despite being the union of countably many metrizable subspaces, has covering dimension equal to 1 and inductive dimensions equal to 2.