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.
About remainders in compactifications of homogeneous spaces
D. Basile, Angelo Bella (2009)
Commentationes Mathematicae Universitatis Carolinae
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We prove a dichotomy theorem for remainders in compactifications of homogeneous spaces: given a homogeneous space , every remainder of is either realcompact and meager or Baire. In addition we show that two other recent dichotomy theorems for remainders of topological groups due to Arhangel’skii cannot be extended to homogeneous spaces.