Displaying similar documents to “About remainders in compactifications of 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 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.

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.

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.

Tightness and resolvability

Angelo Bella, Viacheslav I. Malykhin (1998)

Commentationes Mathematicae Universitatis Carolinae

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We prove resolvability and maximal resolvability of topological spaces having countable tightness with some additional properties. For this purpose, we introduce some new versions of countable tightness. We also construct a couple of examples of irresolvable spaces.

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...

Closed embeddings into complements of Σ -products

Aleksander V. Arhangel'skii, Miroslav Hušek (2008)

Commentationes Mathematicae Universitatis Carolinae

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In some sense, a dual property to that of Valdivia compact is considered, namely the property to be embedded as a closed subspace into a complement of a Σ -subproduct of a Tikhonov cube. All locally compact spaces are co-Valdivia spaces (and only those among metrizable spaces or spaces having countable type). There are paracompact non-locally compact co-Valdivia spaces. A possibly new type of ultrafilters lying in between P-ultrafilters and weak P-ultrafilters is introduced. Under Martin...