Pseudo-boundaries and pseudo-interiors for topological convexities

M. Van de Vel

Displaying similar documents to “Pseudo-boundaries and pseudo-interiors for topological convexities”

Continuous pseudo-hairy spaces and continuous pseudo-fans

Janusz R. Prajs (2002)

Fundamenta Mathematicae

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A compact metric space X̃ is said to be a continuous pseudo-hairy space over a compact space X ⊂ X̃ provided there exists an open, monotone retraction $r : X ̃ \binom{o n t o}{⟶} X$ such that all fibers $r^{- 1} (x)$ are pseudo-arcs and any continuum in X̃ joining two different fibers of r intersects X. A continuum $Y_{X}$ is called a continuous pseudo-fan of a compactum X if there are a point $c \in Y_{X}$ and a family ℱ of pseudo-arcs such that $⋃ ℱ = Y_{X}$ , any subcontinuum of $Y_{X}$ intersecting two different elements of ℱ contains c, and ℱ is homeomorphic...

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 $h ¹_{w}$ .

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...

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...

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...

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 $D$ .

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.

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.

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...

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...

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...

$R_{0}$ and $R_{1}$ topological spaces

C. Dorsett (1978)

Matematički Vesnik

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On $R_{0}$ and $R_{1}$ topological spaces

D. Janković (1981)

Matematički Vesnik

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A note on $R_{0}$ and $R_{1}$ topological spaces

M. R. Žižović (1986)

Matematički Vesnik

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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 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.

A note on $R_{0}$ -topological spaces

K. K. Dube (1974)

Matematički Vesnik

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Remarks on flat and differential $K$ -theory

Man-Ho Ho (2014)

Annales mathématiques Blaise Pascal

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In this note we prove some results in flat and differential $K$ -theory. The first one is a proof of the compatibility of the differential topological index and the flat topological index by a direct computation. The second one is the explicit isomorphisms between Bunke-Schick differential $K$ -theory and Freed-Lott differential $K$ -theory.

Nonnormality of remainders of some topological groups

Aleksander V. Arhangel&#039;skii, J. van Mill (2016)

Commentationes Mathematicae Universitatis Carolinae

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It is known that every remainder of a topological group is Lindelöf or pseudocompact. Motivated by this result, we study in this paper when a topological group $G$ has a normal remainder. In a previous paper we showed that under mild conditions on $G$ , the Continuum Hypothesis implies that if the Čech-Stone remainder $G^{*}$ of $G$ is normal, then it is Lindelöf. Here we continue this line of investigation, mainly for the case of precompact groups. We show that no pseudocompact group, whose weight...