Every paracompact $C^m$-manifold modelled on the infinite countable product of lines is $C^m$-stable

Z. Ogrodzka

Displaying similar documents to “Every paracompact $C^{m}$ -manifold modelled on the infinite countable product of lines is $C^{m}$ -stable”

Characterizations of $z$ -Lindelöf spaces

Ahmad Al-Omari, Takashi Noiri (2017)

Archivum Mathematicum

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A topological space $(X, τ)$ is said to be $z$ -Lindelöf [1] if every cover of $X$ by cozero sets of $(X, τ)$ admits a countable subcover. In this paper, we obtain new characterizations and preservation theorems of $z$ -Lindelöf spaces.

A new Lindelöf space with points $G_{δ}$

Alan S. Dow (2015)

Commentationes Mathematicae Universitatis Carolinae

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We prove that $♦^{*}$ implies there is a zero-dimensional Hausdorff Lindelöf space of cardinality $2^{ℵ_{1}}$ which has points $G_{δ}$ . In addition, this space has the property that it need not be Lindelöf after countably closed forcing.

On hereditary normality of $ω^{*}$ , Kunen points and character $ω_{1}$

Sergei Logunov (2021)

Commentationes Mathematicae Universitatis Carolinae

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We show that $ω^{*} ∖ {p}$ is not normal, if $p$ is a limit point of some countable subset of $ω^{*}$ , consisting of points of character $ω_{1}$ . Moreover, such a point $p$ is a Kunen point and a super Kunen point.

A note on star Lindelöf, first countable and normal spaces

Wei-Feng Xuan (2017)

Mathematica Bohemica

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A topological space $X$ is said to be star Lindelöf if for any open cover $𝒰$ of $X$ there is a Lindelöf subspace $A \subset X$ such that $St (A, 𝒰) = X$ . The “extent” $e (X)$ of $X$ is the supremum of the cardinalities of closed discrete subsets of $X$ . We prove that under $V = L$ every star Lindelöf, first countable and normal space must have countable extent. We also obtain an example under $MA + \neg CH$ , which shows that a star Lindelöf, first countable and normal space may not have countable extent.

A note on spaces with countable extent

Yan-Kui Song (2017)

Commentationes Mathematicae Universitatis Carolinae

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Let $P$ be a topological property. A space $X$ is said to be star P if whenever $𝒰$ is an open cover of $X$ , there exists a subspace $A \subseteq X$ with property $P$ such that $X = S t (A, 𝒰)$ . In this note, we construct a Tychonoff pseudocompact SCE-space which is not star Lindelöf, which gives a negative answer to a question of Rojas-Sánchez and Tamariz-Mascarúa.

Non-normality points and nice spaces

Sergei Logunov (2021)

Commentationes Mathematicae Universitatis Carolinae

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J. Terasawa in " $β X - {p}$ are non-normal for non-discrete spaces $X$ " (2007) and the author in “On non-normality points and metrizable crowded spaces” (2007), independently showed for any metrizable crowded space $X$ that each point $p$ of its Čech–Stone remainder $X^{*}$ is a non-normality point of $β X$ . We introduce a new class of spaces, named nice spaces, which contains both of Sorgenfrey line and every metrizable crowded space. We obtain the result above for every nice space.

On starshapedness of the union of closed sets in $R^{n}$

Krzysztof Kołodziejczyk (1987)

Colloquium Mathematicae

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Stable solutions of $- Δ u = f (u)$ in $ℝ^{N}$

Louis Dupaigne, Alberto Farina (2010)

Journal of the European Mathematical Society

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Several Liouville-type theorems are presented for stable solutions of the equation $- Δ u = f (u)$ in $ℝ^{N}$ , where $f > 0$ is a general convex, nondecreasing function. Extensions to solutions which are merely stable outside a compact set are discussed.

On a certain property of solution of the equation $u_{t} = u_{x x} + f (x, t, u)$

Z. Knap (1970)

Annales Polonici Mathematici

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Compactness in $C_{s} (T)$ and Applications

Richard Haydon (1972)

Publications du Département de mathématiques (Lyon)

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Some types of points in $N^{*}$

Gryzlov, A.

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On Szymański theorem on hereditary normality of $β ω$

Sergei Logunov (2022)

Commentationes Mathematicae Universitatis Carolinae

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We discuss the following result of A. Szymański in “Retracts and non-normality points" (2012), Corollary 3.5.: If $F$ is a closed subspace of $ω^{*}$ and the $π$ -weight of $F$ is countable, then every nonisolated point of $F$ is a non-normality point of $ω^{*}$ . We obtain stronger results for all types of points, excluding the limits of countable discrete sets considered in “Some non-normal subspaces of the Čech–Stone compactification of a discrete space” (1980) by A. Błaszczyk and A. Szymański. Perhaps...

The Niemytzki plane is $ϰ$ -metrizable

Wojciech Bielas, Andrzej Kucharski, Szymon Plewik (2021)

Mathematica Bohemica

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We prove that the Niemytzki plane is $ϰ$ -metrizable and we try to explain the differences between the concepts of a stratifiable space and a $ϰ$ -metrizable space. Also, we give a characterisation of $ϰ$ -metrizable spaces which is modelled on the version described by Chigogidze.

Геометрическая теория состояний, граница фон Неймана, двойственность $C^{*}$ -алгерб

А.М. Вершик (1972)

Zapiski naucnych seminarov Leningradskogo

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Displaying similar documents to “Every paracompact C m -manifold modelled on the infinite countable product of lines is C m -stable”

Displaying similar documents to “Every paracompact $C^{m}$ -manifold modelled on the infinite countable product of lines is $C^{m}$ -stable”