Displaying similar documents to “The theorem of the complement for a quasi subanalytic set”

Quasi-completeness on the Spaces of Holomorphic Germs

Roberto Luiz Soraggi (1981)

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

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Sia E uno spazio D F riflessivo e sia K un compatto di E . Si dimostra che lo spazio dei germi olomorfi su K , con la topologia naturale, è un limite induttivo regolare e quasi completo purché lo spazio dei germi olomorfi all'origine sia un limite induttivo regolare.

Real deformations and invariants of map-germs

J. H. Rieger, M. A. S. Ruas, R. Wik Atique (2008)

Banach Center Publications

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A stable deformation f t of a real map-germ f : , 0 p , 0 is said to be an M-deformation if all isolated stable (local and multi-local) singularities of its complexification f t are real. A related notion is that of a good real perturbation f t of f (studied e.g. by Mond and his coworkers) for which the homology of the image (for n < p) or discriminant (for n ≥ p) of f t coincides with that of f C t . The class of map germs having an M-deformation is, in some sense, much larger than the one having a good...

Quasi-completeness on the Spaces of Holomorphic Germs

Roberto Luiz Soraggi (1981)

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

Similarity:

Sia E uno spazio D F riflessivo e sia K un compatto di E . Si dimostra che lo spazio dei germi olomorfi su K , con la topologia naturale, è un limite induttivo regolare e quasi completo purché lo spazio dei germi olomorfi all'origine sia un limite induttivo regolare.

Boundedness of sublinear operators in Triebel-Lizorkin spaces via atoms

Liguang Liu, Dachun Yang (2009)

Studia Mathematica

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Let s ∈ ℝ, p ∈ (0,1] and q ∈ [p,∞). It is proved that a sublinear operator T uniquely extends to a bounded sublinear operator from the Triebel-Lizorkin space p , q s ( ) to a quasi-Banach space ℬ if and only if sup | | T ( a ) | | : a is an infinitely differentiable (p,q,s)-atom of p , q s ( ) < ∞, where the (p,q,s)-atom of p , q s ( ) is as defined by Han, Paluszyński and Weiss.

Stratified Whitney jets and tempered ultradistributions on the subanalytic site

N. Honda, G. Morando (2011)

Bulletin de la Société Mathématique de France

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In this paper we introduce the sheaf of stratified Whitney jets of Gevrey order on the subanalytic site relative to a real analytic manifold X . Then, we define stratified ultradistributions of Beurling and Roumieu type on X . In the end, by means of stratified ultradistributions, we define tempered-stratified ultradistributions and we prove two results. First, if X is a real surface, the tempered-stratified ultradistributions define a sheaf on the subanalytic site relative to X . Second,...

J -holomorphic discs and real analytic hypersurfaces

William Alexandre, Emmanuel Mazzilli (2014)

Annales de l’institut Fourier

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We give in 6 a real analytic almost complex structure J , a real analytic hypersurface M and a vector v in the Levi null set at 0 of M , such that there is no germ of J -holomorphic disc γ included in M with γ ( 0 ) = 0 and γ x ( 0 ) = v , although the Levi form of M has constant rank. Then for any hypersurface M and any complex structure J , we give sufficient conditions under which there exists such a germ of disc.

C 1 self-maps on closed manifolds with finitely many periodic points all of them hyperbolic

Jaume Llibre, Víctor F. Sirvent (2016)

Mathematica Bohemica

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Let X be a connected closed manifold and f a self-map on X . We say that f is almost quasi-unipotent if every eigenvalue λ of the map f * k (the induced map on the k -th homology group of X ) which is neither a root of unity, nor a zero, satisfies that the sum of the multiplicities of λ as eigenvalue of all the maps f * k with k odd is equal to the sum of the multiplicities of λ as eigenvalue of all the maps f * k with k even. We prove that if f is C 1 having finitely many periodic points all of them...

Some results on quasi-t-dual Baer modules

Rachid Tribak, Yahya Talebi, Mehrab Hosseinpour (2023)

Commentationes Mathematicae Universitatis Carolinae

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Let R be a ring and let M be an R -module with S = End R ( M ) . Consider the preradical Z ¯ for the category of right R -modules Mod- R introduced by Y. Talebi and N. Vanaja in 2002 and defined by Z ¯ ( M ) = { U M : M / U is small in its injective hull } . The module M is called quasi-t-dual Baer if ϕ ϕ ( Z ¯ 2 ( M ) ) is a direct summand of M for every two-sided ideal of S , where Z ¯ 2 ( M ) = Z ¯ ( Z ¯ ( M ) ) . In this paper, we show that M is quasi-t-dual Baer if and only if Z ¯ 2 ( M ) is a direct summand of M and Z ¯ 2 ( M ) is a quasi-dual Baer module. It is also shown that any direct...

On a problem concerning quasianalytic local rings

Hassan Sfouli (2014)

Annales Polonici Mathematici

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Let (ₙ)ₙ be a quasianalytic differentiable system. Let m ∈ ℕ. We consider the following problem: let f m and f̂ be its Taylor series at 0 m . Split the set m of exponents into two disjoint subsets A and B, m = A B , and decompose the formal series f̂ into the sum of two formal series G and H, supported by A and B, respectively. Do there exist g , h m with Taylor series at zero G and H, respectively? The main result of this paper is the following: if we have a positive answer to the above problem for some...

On the inclusions of X Φ spaces

Seyyed Mohammad Tabatabaie, Alireza Bagheri Salec (2023)

Mathematica Bohemica

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We give some equivalent conditions (independent from the Young functions) for inclusions between some classes of X Φ spaces, where Φ is a Young function and X is a quasi-Banach function space on a σ -finite measure space ( Ω , 𝒜 , μ ) .

Order boundedness and weak compactness of the set of quasi-measure extensions of a quasi-measure

Zbigniew Lipecki (2015)

Commentationes Mathematicae Universitatis Carolinae

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Let 𝔐 and be algebras of subsets of a set Ω with 𝔐 , and denote by E ( μ ) the set of all quasi-measure extensions of a given quasi-measure μ on 𝔐 to . We give some criteria for order boundedness of E ( μ ) in b a ( ) , in the general case as well as for atomic μ . Order boundedness implies weak compactness of E ( μ ) . We show that the converse implication holds under some assumptions on 𝔐 , and μ or μ alone, but not in general.

Special sets of reals and weak forms of normality on Isbell--Mrówka spaces

Vinicius de Oliveira Rodrigues, Victor dos Santos Ronchim, Paul J. Szeptycki (2023)

Commentationes Mathematicae Universitatis Carolinae

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We recall some classical results relating normality and some natural weakenings of normality in Ψ -spaces over almost disjoint families of branches in the Cantor tree to special sets of reals like Q -sets, λ -sets and σ -sets. We introduce a new class of special sets of reals which corresponds to the corresponding almost disjoint family of branches being 0 -separated. This new class fits between λ -sets and perfectly meager sets. We also discuss conditions for an almost disjoint family 𝒜 being...

On some representations of almost everywhere continuous functions on m

Ewa Strońska (2006)

Colloquium Mathematicae

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It is proved that the following conditions are equivalent: (a) f is an almost everywhere continuous function on m ; (b) f = g + h, where g,h are strongly quasicontinuous on m ; (c) f = c + gh, where c ∈ ℝ and g,h are strongly quasicontinuous on m .

Norm continuity of pointwise quasi-continuous mappings

Alireza Kamel Mirmostafaee (2018)

Mathematica Bohemica

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Let X be a Baire space, Y be a compact Hausdorff space and ϕ : X C p ( Y ) be a quasi-continuous mapping. For a proximal subset H of Y × Y we will use topological games 𝒢 1 ( H ) and 𝒢 2 ( H ) on Y × Y between two players to prove that if the first player has a winning strategy in these games, then ϕ is norm continuous on a dense G δ subset of X . It follows that if Y is Valdivia compact, each quasi-continuous mapping from a Baire space X to C p ( Y ) is norm continuous on a dense G δ subset of X .

Foliated structure of the Kuranishi space and isomorphisms of deformation families of compact complex manifolds

Laurent Meersseman (2011)

Annales scientifiques de l'École Normale Supérieure

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Consider the following uniformization problem. Take two holomorphic (parametrized by some analytic set defined on a neighborhood of 0 in p , for some p &gt; 0 ) or differentiable (parametrized by an open neighborhood of 0 in p , for some p &gt; 0 ) deformation families of compact complex manifolds. Assume they are pointwise isomorphic, that is for each point t of the parameter space, the fiber over t of the first family is biholomorphic to the fiber over t of the second family. Then, under which conditions...

On Hattori spaces

A. Bouziad, E. Sukhacheva (2017)

Commentationes Mathematicae Universitatis Carolinae

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For a subset A of the real line , Hattori space H ( A ) is a topological space whose underlying point set is the reals and whose topology is defined as follows: points from A are given the usual Euclidean neighborhoods while remaining points are given the neighborhoods of the Sorgenfrey line. In this paper, among other things, we give conditions on A which are sufficient and necessary for H ( A ) to be respectively almost Čech-complete, Čech-complete, quasicomplete, Čech-analytic and weakly separated...

Order convexity and concavity of Lorentz spaces Λ p , w , 0 < p < ∞

Anna Kamińska, Lech Maligranda (2004)

Studia Mathematica

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We study order convexity and concavity of quasi-Banach Lorentz spaces Λ p , w , where 0 < p < ∞ and w is a locally integrable positive weight function. We show first that Λ p , w contains an order isomorphic copy of l p . We then present complete criteria for lattice convexity and concavity as well as for upper and lower estimates for Λ p , w . We conclude with a characterization of the type and cotype of Λ p , w in the case when Λ p , w is a normable space.