Continuous pseudo-hairy spaces and continuous pseudo-fans

Janusz R. Prajs

Displaying similar documents to “Continuous pseudo-hairy spaces and continuous pseudo-fans”

Pseudo-boundaries and pseudo-interiors for topological convexities

M. Van de Vel

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CONTENTS0. Introduction......... .............................................................51. Topological convexity structures.......................................62. Half-spaces and related results......................................123. Pseudo-boundaries........................................................254. The Krein-Milman theorem.............................................335. Pseudo-interiority...........................................................406. The existence...

On a question of Demailly-Peternell-Schneider

Meng Chen, Qi Zhang (2013)

Journal of the European Mathematical Society

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We give an affirmative answer to an open question posed by Demailly-Peternell-Schneider in 2001 and recently by Peternell. Let $f : X \to Y$ be a surjective morphism from a log canonical pair $(X, D)$ onto a $ℚ$ -Gorenstein variety $Y$ . If $- (K_{X} + D)$ is nef, we show that $- K_{Y}$ is pseudo-effective.

The continuity of pseudo-differential operators on weighted local Hardy spaces

Ming-Yi Lee, Chin-Cheng Lin, Ying-Chieh Lin (2010)

Studia Mathematica

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We first show that a linear operator which is bounded on $L ²_{w}$ with w ∈ A₁ can be extended to a bounded operator on the weighted local Hardy space $h ¹_{w}$ if and only if this operator is uniformly bounded on all $h ¹_{w}$ -atoms. As an application, we show that every pseudo-differential operator of order zero has a bounded extension to $h ¹_{w}$ .

Intrinsic pseudo-volume forms for logarithmic pairs

Thomas Dedieu (2010)

Bulletin de la Société Mathématique de France

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We study an adaptation to the logarithmic case of the Kobayashi-Eisenman pseudo-volume form, or rather an adaptation of its variant defined by Claire Voisin, for which she replaces holomorphic maps by holomorphic $K$ -correspondences. We define an intrinsic logarithmic pseudo-volume form $Φ_{X, D}$ for every pair $(X, D)$ consisting of a complex manifold $X$ and a normal crossing Weil divisor $D$ on $X$ , the positive part of which is reduced. We then prove that $Φ_{X, D}$ is generically non-degenerate when $X$ is projective...

Pseudo-real principal Higgs bundles on compact Kähler manifolds

Indranil Biswas, Oscar García-Prada, Jacques Hurtubise (2014)

Annales de l’institut Fourier

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Let $X$ be a compact connected Kähler manifold equipped with an anti-holomorphic involution which is compatible with the Kähler structure. Let $G$ be a connected complex reductive affine algebraic group equipped with a real form $σ_{G}$ . We define pseudo-real principal $G$ -bundles on $X$ . These are generalizations of real algebraic principal $G$ -bundles over a real algebraic variety. Next we define stable, semistable and polystable pseudo-real principal $G$ -bundles. Their relationships with the usual...

Domain representability of $C_{p} (X)$

Harold Bennett, David Lutzer (2008)

Fundamenta Mathematicae

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Let $C_{p} (X)$ be the space of continuous real-valued functions on X, with the topology of pointwise convergence. We consider the following three properties of a space X: (a) $C_{p} (X)$ is Scott-domain representable; (b) $C_{p} (X)$ is domain representable; (c) X is discrete. We show that those three properties are mutually equivalent in any normal T₁-space, and that properties (a) and (c) are equivalent in any completely regular pseudo-normal space. For normal spaces, this generalizes the recent result of Tkachuk...

The discriminant and oscillation lengths for contact and Legendrian isotopies

Vincent Colin, Sheila Sandon (2015)

Journal of the European Mathematical Society

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We define an integer-valued non-degenerate bi-invariant metric (the discriminant metric) on the universal cover of the identity component of the contactomorphism group of any contact manifold. This metric has a very simple geometric definition, based on the notion of discriminant points of contactomorphisms. Using generating functions we prove that the discriminant metric is unbounded for the standard contact structures on $ℝ^{2 n} \times S^{1}$ and $ℝ P^{2 n + 1}$ . On the other hand we also show by elementary arguments...

Algebraic bounds on analytic multiplier ideals

Brian Lehmann (2014)

Annales de l’institut Fourier

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Given a pseudo-effective divisor $L$ we construct the diminished ideal $𝒥_{σ} (L)$ , a “continuous” extension of the asymptotic multiplier ideal for big divisors to the pseudo-effective boundary. Our main theorem shows that for most pseudo-effective divisors $L$ the multiplier ideal $𝒥 (h_{\min})$ of the metric of minimal singularities on $𝒪_{X} (L)$ is contained in $𝒥_{σ} (L)$ . We also characterize abundant divisors using the diminished ideal, indicating that the geometric and analytic information should coincide.

Semigroups generated by certain pseudo-differential operators on the half-space $ℝ_{0 +}^{n + 1}$

Victoria Knopova (2004)

Colloquium Mathematicae

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The aim of the paper is two-fold. First, we investigate the ψ-Bessel potential spaces on $ℝ_{0 +}^{n + 1}$ and study some of their properties. Secondly, we consider the fractional powers of an operator of the form $- A_{\pm} = - ψ (D_{x^{'}}) \pm \partial / (\partial x_{n + 1})$ , $(x^{'}, x_{n + 1}) \in ℝ_{0 +}^{n + 1}$ , where $ψ (D_{x^{'}})$ is an operator with real continuous negative definite symbol ψ: ℝⁿ → ℝ. We define the domain of the operator $- {(- A_{\pm})}^{α}$ and prove that with this domain it generates an $L_{p}$ -sub-Markovian semigroup.

Adding or removing an element from a pseudo-symmetric numerical semigroup

J. C. Rosales (2006)

Bollettino dell'Unione Matematica Italiana

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If $S$ is a pseudo-symmetric numerical semigroup, $g$ is its Frobenius number and $S$ is a minimal generator of $S$ , then $S\cup\{g\}$ , $S\setminus\{g\}$ S and $S\cup\{\frac{1}{2}g,g\}$ are also numerical semigroups. In this paper we study these constructions.

On two-to-one continuous functions

J. Mioduszewski

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CONTENTSIntroduction................................................................................................................................................................................3I. General properties of k-to-one functions on locally compact spaces1. Multi-valued functions Ф and ψ......................................................................................................................................... 62. The proof of (I.11)..................................................................................................................................................................

On non-Uniqueness of Complex Geodesies in Convex Bounded Domains

Graziano Gentili (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Si studiano «combinazioni convesse complesse» per mappe olomorfe dal disco unità di $\mathbb{C}$ in un dominio convesso limitato $D$ di uno spazio di Banach complesso $E$ , e se ne traggono conseguenze sul carattere globale della non unicità per le geodetiche complesse di $D$ .

On a question of $C_{c} (X)$

A. R. Olfati (2016)

Commentationes Mathematicae Universitatis Carolinae

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In this short article we answer the question posed in Ghadermazi M., Karamzadeh O.A.S., Namdari M., On the functionally countable subalgebra of $C (X)$ , Rend. Sem. Mat. Univ. Padova 129 (2013), 47–69. It is shown that $C_{c} (X)$ is isomorphic to some ring of continuous functions if and only if $υ_{0} X$ is functionally countable. For a strongly zero-dimensional space $X$ , this is equivalent to say that $X$ is functionally countable. Hence for every $P$ -space it is equivalent to pseudo- $ℵ_{0}$ -compactness.

Extending generalized Whitney maps

Ivan Lončar (2017)

Archivum Mathematicum

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For metrizable continua, there exists the well-known notion of a Whitney map. If $X$ is a nonempty, compact, and metric space, then any Whitney map for any closed subset of $2^{X}$ can be extended to a Whitney map for $2^{X}$ [3, 16.10 Theorem]. The main purpose of this paper is to prove some generalizations of this theorem.

Weighted local Orlicz-Hardy spaces with applications to pseudo-differential operators

Dachun Yang, Sibei Yang

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Let Φ be a concave function on (0,∞) of strictly critical lower type index $p_{Φ} \in (0, 1]$ and $ω \in A_{\infty}^{l o c} (ℝ ⁿ)$ (the class of local weights introduced by V. S. Rychkov). We introduce the weighted local Orlicz-Hardy space $h_{ω}^{Φ} (ℝ ⁿ)$ via the local grand maximal function. Let $ρ (t) \equiv t^{- 1} / Φ^{- 1} (t^{- 1})$ for all t ∈ (0,∞). We also introduce the BMO-type space $b m o_{ρ, ω} (ℝ ⁿ)$ and establish the duality between $h_{ω}^{Φ} (ℝ ⁿ)$ and $b m o_{ρ, ω} (ℝ ⁿ)$ . Characterizations of $h_{ω}^{Φ} (ℝ ⁿ)$ , including the atomic characterization, the local vertical and the local nontangential maximal function characterizations, are...

Shells of monotone curves

Josef Mikeš, Karl Strambach (2015)

Czechoslovak Mathematical Journal

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We determine in $ℝ^{n}$ the form of curves $C$ corresponding to strictly monotone functions as well as the components of affine connections $\nabla$ for which any image of $C$ under a compact-free group $Ω$ of affinities containing the translation group is a geodesic with respect to $\nabla$ . Special attention is paid to the case that $Ω$ contains many dilatations or that $C$ is a curve in $ℝ^{3}$ . If $C$ is a curve in $ℝ^{3}$ and $Ω$ is the translation group then we calculate not only the components of the curvature and the Weyl...

On the volume of a pseudo-effective class and semi-positive properties of the Harder-Narasimhan filtration on a compact Hermitian manifold

Zhiwei Wang (2016)

Annales Polonici Mathematici

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This paper divides into two parts. Let (X,ω) be a compact Hermitian manifold. Firstly, if the Hermitian metric ω satisfies the assumption that $\partial \partial ̅ ω^{k} = 0$ for all k, we generalize the volume of the cohomology class in the Kähler setting to the Hermitian setting, and prove that the volume is always finite and the Grauert-Riemenschneider type criterion holds true, which is a partial answer to a conjecture posed by Boucksom. Secondly, we observe that if the anticanonical bundle $K_{X}^{- 1}$ is nef, then for...

Singular arc-like continua

Tadeusz Maćkowiak

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CONTENTSIntroduction.......................................................................................................51. Preliminaries.................................................................................................6 A. Mappings....................................................................................................6 B. Arc-like continua.........................................................................................8 C. Pseudosuspensions...................................................................................8 D....

Geometric stability of the cotangent bundle and the universal cover of a projective manifold

Frédéric Campana, Thomas Peternell (2011)

Bulletin de la Société Mathématique de France

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We first prove a strengthening of Miyaoka’s generic semi-positivity theorem: the quotients of the tensor powers of the cotangent bundle of a non-uniruled complex projective manifold $X$ have a pseudo-effective (instead of generically nef) determinant. A first consequence is that $X$ is of general type if its cotangent bundle contains a subsheaf with ‘big’ determinant. Among other applications, we deduce that if the universal cover of $X$ is not covered by compact positive-dimensional analytic...

On affinity of Peano type functions

Tomasz Słonka (2012)

Colloquium Mathematicae

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We show that if n is a positive integer and $2^{ℵ ₀} \leq ℵ ₙ$ , then for every positive integer m and for every real constant c > 0 there are functions $f ₁, . . ., f_{n + m} : ℝ ⁿ \to ℝ$ such that $(f ₁, . . ., f_{n + m}) (ℝ ⁿ) = ℝ^{n + m}$ and for every x ∈ ℝⁿ there exists a strictly increasing sequence (i₁,...,iₙ) of numbers from 1,...,n+m and a w ∈ ℤⁿ such that $(f_{i ₁}, . . ., f_{i ₙ}) (y) = y + w$ for $y \in x + (- c, c) \times ℝ^{n - 1}$ .

A continuum $X$ such that $C (X)$ is not continuously homogeneous

Alejandro Illanes (2016)

Commentationes Mathematicae Universitatis Carolinae

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A metric continuum $X$ is said to be continuously homogeneous provided that for every two points $p, q \in X$ there exists a continuous surjective function $f : X \to X$ such that $f (p) = q$ . Answering a question by W.J. Charatonik and Z. Garncarek, in this paper we show a continuum $X$ such that the hyperspace of subcontinua of $X$ , $C (X)$ , is not continuously homogeneous.

On Dimensionsgrad, resolutions, and chainable continua

Michael G. Charalambous, Jerzy Krzempek (2010)

Fundamenta Mathematicae

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For each natural number n ≥ 1 and each pair of ordinals α,β with n ≤ α ≤ β ≤ ω(⁺), where ω(⁺) is the first ordinal of cardinality ⁺, we construct a continuum $S_{n, α, β}$ such that (a) $d i m S_{n, α, β} = n$ ; (b) $t r D g S_{n, α, β} = t r D g o S_{n, α, β} = α$ ; (c) $t r i n d S_{n, α, β} = t r I n d ₀ S_{n, α, β} = β$ ; (d) if β < ω(⁺), then $S_{n, α, β}$ is separable and first countable; (e) if n = 1, then $S_{n, α, β}$ can be made chainable or hereditarily decomposable; (f) if α = β < ω(⁺), then $S_{n, α, β}$ can be made hereditarily indecomposable; (g) if n = 1 and α = β < ω(⁺), then $S_{n, α, β}$ can be made chainable and hereditarily indecomposable. In...