A generalized -porous set with a small complement.
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Tišer, Jaroslav (2005)
Abstract and Applied Analysis
Mar Fenoy-Muñoz, José Luis Gámez-Merino, Gustavo A. Muñoz-Fernández, Eva Sáez-Maestro (2017)
Open Mathematics
This expository paper focuses on the study of extreme surjective functions in ℝℝ. We present several different types of extreme surjectivity by providing examples and crucial properties. These examples help us to establish a hierarchy within the different classes of surjectivity we deal with. The classes presented here are: everywhere surjective functions, strongly everywhere surjective functions, κ-everywhere surjective functions, perfectly everywhere surjective functions and Jones functions. The...
John A. Baker (1985)
Aequationes mathematicae
Luděk Zajíček (1983)
Commentationes Mathematicae Universitatis Carolinae
Eva Matoušková (1999)
Studia Mathematica
Every separable infinite-dimensional superreflexive Banach space admits an equivalent norm which is Fréchet differentiable only on an Aronszajn null set.
Frank Oertel (2015)
Dependence Modeling
We revisit Sklar’s Theorem and give another proof, primarily based on the use of right quantile functions. To this end we slightly generalise the distributional transform approach of Rüschendorf and facilitate some new results including a rigorous characterisation of an almost surely existing “left-invertibility” of distribution functions.
Zdzisław Denkowski (1980)
Annales Polonici Mathematici
Girgensohn, Roland (2001)
Mathematica Pannonica
Olivier Le Gal, Jean-Philippe Rolin (2009)
Annales de l’institut Fourier
We present an example of an o-minimal structure which does not admit cellular decomposition. To this end, we construct a function whose germ at the origin admits a representative for each integer , but no representative. A number theoretic condition on the coefficients of the Taylor series of then insures the quasianalyticity of some differential algebras induced by . The o-minimality of the structure generated by is deduced from this quasianalyticity property.
Daniel Boichu (1994)
Colloquium Mathematicae
En dimension 1 on analyse la fonction irrégulière (p entier ≥ 2) en un point de dérivabilité (π est un tel point) et on démontre que le terme d’erreur est un chirp de classe (1 + 1/(2p-2), 1/(p-1), (p-1)/p). La fonction r(x) est dans l’espace 2-microlocal si et seulement si s+s’ ≤ 1 - 1/p et ps+s’≤ p - 1/2. En dimension 2, on obtient en (π,π) l’existence d’un plan tangent pour la surface dès que γ>1.
Jan Malý, Luděk Zajíček (1991)
Fundamenta Mathematicae
Michael J. Evans (1987)
Colloquium Mathematicae
Marcin Pilipczuk (2011)
Fundamenta Mathematicae
We give a characterization of compact subsets of finite unions of disjoint finite-length curves in ℝⁿ with ω-continuous derivative and without self-intersections. Intuitively, our condition can be formulated as follows: there exists a finite set of regular curves covering a compact set K iff every triple of points of K behaves like a triple of points of a regular curve. This work was inspired by theorems by Jones, Okikiolu, Schul and others that characterize compact subsets of...
H.-H. Kairies (1990)
Elemente der Mathematik
Michel Balazard, Bruno Martin (2012)
Fundamenta Mathematicae
We describe the average behaviour of the Brjuno function Φ in the neighbourhood of any given point of the unit interval. In particular, we show that the Lebesgue set of Φ is the set of Brjuno numbers and we find the asymptotic behaviour of the modulus of continuity of the integral of Φ.
Pallaschke, Diethard, Urbański, Ryszard (1997)
Journal of Convex Analysis
Ladislav Mišík (1971)
Pokroky matematiky, fyziky a astronomie
T. W. Körner (1990)
Colloquium Mathematicae
Timofte, Vlad (2004)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Penot, Jean-Paul, Zălinescu, Constantin (2000)
Journal of Convex Analysis
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