Countable dense homogeneous spaces
R. Bennett (1972)
Fundamenta Mathematicae
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Displaying similar documents to “Countable dense homogeneity and n-homogeneity”
Countable dense homogeneous spaces
Baire category in spaces of probability measures
Jack Brown (1977)
Fundamenta Mathematicae
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A note on countable dense homogeneity
Ben Fitzpatrick (1972)
Fundamenta Mathematicae
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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...
Lusin properties in the product space
G. Cox (1980)
Fundamenta Mathematicae
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On Countable Dense and Strong Local Homogeneity
Jan van Mill (2005)
Bulletin of the Polish Academy of Sciences. Mathematics
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We present an example of a connected, Polish, countable dense homogeneous space X that is not strongly locally homogeneous. In fact, a nontrivial homeomorphism of X is the identity on no nonempty open subset of X.
Zero-dimensional countable dense unions of Z-sets in the Hilbert cube
D. Curtis, Jan van Mill (1983)
Fundamenta Mathematicae
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Characterizations of the countable infinite product of rationals and some related problems
van Engelen, Fons
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A countable dense homogeneous space with a dense rigid open subspace
Jan van Mill (2008)
Fundamenta Mathematicae
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We show that there is a Polish space which is countable dense homogeneous but contains a dense open rigid connected subset. This answers several questions of Fitzpatrick and Zhou.