Displaying similar documents to “A Polish AR-Space with no Nontrivial Isotopy”

On countable dense and strong n-homogeneity

Jan van Mill (2011)

Fundamenta Mathematicae

Similarity:

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.

On Countable Dense and Strong Local Homogeneity

Jan van Mill (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

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.

About remainders in compactifications of homogeneous spaces

D. Basile, Angelo Bella (2009)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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 homogeneous filters and the Menger covering property

Dušan Repovš, Lyubomyr Zdomskyy, Shuguo Zhang (2014)

Fundamenta Mathematicae

Similarity:

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.

Countable homogeneous coloured partial orders

Susana Torrezão de Sousa, J. K. Truss

Similarity:

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

Countable dense homogeneity and λ-sets

Rodrigo Hernández-Gutiérrez, Michael Hrušák, Jan van Mill (2014)

Fundamenta Mathematicae

Similarity:

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...

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

Similarity:

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...