Displaying similar documents to “On Countable Dense and Strong Local Homogeneity”

On countable dense and strong n-homogeneity

Jan van Mill (2011)

Fundamenta Mathematicae

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We prove that if a space X is countable dense homogeneous and no set of size n-1 separates it, then X is strongly n-homogeneous. Our main result is the construction of an example of a Polish space X that is strongly n-homogeneous for every n, but not countable dense homogeneous.

About Homogeneous Spaces and Conditions of Completeness of Spaces Относно хомогенни пространства и условия за пълнота

Arhangel’skii, Alexander, Choban, Mitrofan, Mihaylova, Ekaterina (2012)

Union of Bulgarian Mathematicians

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Александър В. Архангелски, Митрофан М. Чобан, Екатерина П. Михайлова - Въведени са понятията o-хомогенно пространство, lo-хомогенно пространство, do-хомогенно пространство и co-хомогенно пространство. Показано е, че ако lo-хомогенно пространство X има отворено подпространство, което е q-пълно, то и самото X е q-пълно. Показано е, че ако lo-хомогенно пространство X съдържа навсякъде гъсто екстремално несвързано подпространство, тогава X е екстремално несвързано. In this paper...

Countable dense homogeneous filters and the Menger covering property

Dušan Repovš, Lyubomyr Zdomskyy, Shuguo Zhang (2014)

Fundamenta Mathematicae

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We present a ZFC construction of a non-meager filter which fails to be countable dense homogeneous. This answers a question of Hernández-Gutiérrez and Hrušák. The method of the proof also allows us to obtain for any n ∈ ω ∪ {∞} an n-dimensional metrizable Baire topological group which is strongly locally homogeneous but not countable dense homogeneous.

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 X , every remainder of X 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.

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 homogeneous coloured partial orders

Susana Torrezão de Sousa, J. K. Truss

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We give a classification of all the countable homogeneous coloured partial orders. This generalizes the similar result in the monochromatic case given by Schmerl.

A Polish AR-Space with no Nontrivial Isotopy

Tadeusz Dobrowolski (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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The Polish space Y constructed in [vM1] admits no nontrivial isotopy. Yet, there exists a Polish group that acts transitively on Y.

Open subspaces of countable dense homogeneous spaces

Stephen Watson, Petr Simon (1992)

Fundamenta Mathematicae

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We construct a completely regular space which is connected, locally connected and countable dense homogeneous but not strongly locally homogeneous. The space has an open subset which has a unique cut-point. We use the construction of a C 1 -diffeomorphism of the plane which takes one countable dense set to another.

About Homogeneous Spaces and the Baire Property in Remainders Относно хомогенни пространства и свойството на Бер в прираста

Arhangel’skii, Alexander, Choban, Mitrofan, Mihaylova, Ekaterina (2012)

Union of Bulgarian Mathematicians

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Александър В. Архангелски, Митрофан М. Чобан, Екатерина П. Михайлова - В съобщението е продължено изследването на понятията o-хомогенно пространство, lo-хомогенно пространство, do-хомогенно пространство и co-хомогенно пространство. Показано е, че ако co-хомогенното пространство X съдържа Gδ -гъсто Московско подпространство, тогава X е Московско пространство. In this paper we continue the study of the notions of o-homogeneous space, lo-homogeneous space, do-homogeneous space...