The projective limit of the spaces
J. A. Cima, J. R. Harrington, J. A. Pfaltzgraff (1977)
Colloquium Mathematicae
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J. A. Cima, J. R. Harrington, J. A. Pfaltzgraff (1977)
Colloquium Mathematicae
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Josef Vala (1988)
Časopis pro pěstování matematiky
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Fabio Podestà (1987)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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In this work we give a characterization of the projective invariant pseudometric , introduced by H. Wu, for a particular class of real -manifolds; in view of this result, we study the group of projective transformations for the same class of manifolds and we determine the integrated pseudodistance of in open convex regular cones of , endowed with the characteristic metric.
Fabio Podestà (1987)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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In this work we give a characterization of the projective invariant pseudometric , introduced by H. Wu, for a particular class of real -manifolds; in view of this result, we study the group of projective transformations for the same class of manifolds and we determine the integrated pseudodistance of in open convex regular cones of , endowed with the characteristic metric.
Robert Rumely (2015)
Acta Arithmetica
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Let K be a complete, algebraically closed nonarchimedean valued field, and let φ(z) ∈ K(z) have degree d ≥ 2. We study how the resultant of φ varies under changes of coordinates. For γ ∈ GL₂(K), we show that the map factors through a function on the Berkovich projective line, which is piecewise affine and convex up. The minimal resultant is achieved either at a single point in , or on a segment, and the minimal resultant locus is contained in the tree in spanned by the fixed points...
Tamás Terpai (2009)
Banach Center Publications
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We calculate the mapping and obtain a generating system of its kernel. As a corollary, bounds on the codimension of fold maps from real projective spaces to Euclidean space are calculated and the rank of a singular bordism group is determined.
Yves Guivarc'h, Roman Urban (2005)
Studia Mathematica
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Let Γ be a subsemigroup of G = GL(d,ℝ), d > 1. We assume that the action of Γ on is strongly irreducible and that Γ contains a proximal and quasi-expanding element. We describe contraction properties of the dynamics of Γ on at infinity. This amounts to the consideration of the action of Γ on some compact homogeneous spaces of G, which are extensions of the projective space . In the case where Γ is a subsemigroup of GL(d,ℝ) ∩ M(d,ℤ) and Γ has the above properties, we deduce that...
Tien Duc Luu (2013)
Annales de la faculté des sciences de Toulouse Mathématiques
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We prove in this paper the Hölder regularity of Almgren minimal sets of dimension 3 in around a -point and the existence of a point of particular type of a Mumford-Shah minimal set in , which is very close to a . This will give a local description of minimal sets of dimension 3 in around a singular point and a property of Mumford-Shah minimal sets in .
Papa A. Sissokho (2014)
Acta Arithmetica
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A zero-sum sequence over ℤ is a sequence with terms in ℤ that sum to 0. It is called minimal if it does not contain a proper zero-sum subsequence. Consider a minimal zero-sum sequence over ℤ with positive terms and negative terms . We prove that h ≤ ⌊σ⁺/k⌋ and k ≤ ⌊σ⁺/h⌋, where . These bounds are tight and improve upon previous results. We also show a natural partial order structure on the collection of all minimal zero-sum sequences over the set i∈ ℤ : -n ≤ i ≤ n for any positive...
Eva Ferrara Dentice (2018)
Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche
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In the paper (Ferrara Dentice et al., 2004) a complete exposition of the state of the art for lax embeddings of polar spaces of finite rank is presented. As a consequence, we have that if a Grassmann space of dimension 3 and index 1 has a lax embedding in a projective space over a skew–field , then is the Klein quadric defined over a subfield of . In this paper, I examine Grassmann spaces of arbitrary dimension and index having a lax embedding in a projective space.
Jörg Brendle, Sakaé Fuchino (2007)
Fundamenta Mathematicae
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We study combinatorial principles we call the Homogeneity Principle HP(κ) and the Injectivity Principle IP(κ,λ) for regular κ > ℵ₁ and λ ≤ κ which are formulated in terms of coloring the ordinals < κ by reals. These principles are strengthenings of and of I. Juhász, L. Soukup and Z. Szentmiklóssy. Generalizing their results, we show e.g. that IP(ℵ₂,ℵ₁) (hence also IP(ℵ₂,ℵ₂) as well as HP(ℵ₂)) holds in a generic extension of a model of CH by Cohen forcing, and IP(ℵ₂,ℵ₂) (hence...
Beata Kocel-Cynk (2007)
Annales Polonici Mathematici
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We prove that for a finite collection of sets definable in an o-minimal structure there exists a compatible definable stratification such that for any stratum the fibers of its projection onto satisfy the Whitney property with exponent 1.
Abdelhafed Elkhadiri, Hassan Sfouli (2006)
Annales Polonici Mathematici
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We give some examples of polynomially bounded o-minimal expansions of the ordered field of real numbers where the Weierstrass division theorem does not hold in the ring of germs, at the origin of ℝⁿ, of definable functions.
Jana Maříková (2010)
Fundamenta Mathematicae
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Let R be an o-minimal field and V a proper convex subring with residue field k and standard part (residue) map st: V → k. Let be the expansion of k by the standard parts of the definable relations in R. We investigate the definable sets in and conditions on (R,V) which imply o-minimality of . We also show that if R is ω-saturated and V is the convex hull of ℚ in R, then the sets definable in are exactly the standard parts of the sets definable in (R,V).
Beata Deręgowska, Barbara Lewandowska (2014)
Annales Polonici Mathematici
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Let V ⊂ Z be two subspaces of a Banach space X. We define the set of generalized projections by . Now let X = c₀ or , Z:= kerf for some f ∈ X* and (n < m). The main goal of this paper is to discuss existence, uniqueness and strong uniqueness of a minimal generalized projection in this case. Also formulas for the relative generalized projection constant and the strong uniqueness constant will be given (cf. J. Blatter and E. W. Cheney [Ann. Mat. Pura Appl. 101 (1974), 215-227] and...
Koen Thas, Don Zagier (2008)
Journal of the European Mathematical Society
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One of the oldest and most fundamental problems in the theory of finite projective planes is to classify those having a group which acts transitively on the incident point-line pairs (flags). The conjecture is that the only ones are the Desarguesian projective planes (over a finite field). In this paper, we show that non-Desarguesian finite flag-transitive projective planes exist if and only if certain Fermat surfaces have no nontrivial rational points, and formulate several other equivalences...
Andreas Fischer (2008)
Annales Polonici Mathematici
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Given an o-minimal expansion ℳ of a real closed field R which is not polynomially bounded. Let denote the definable indefinitely Peano differentiable functions. If we further assume that ℳ admits cell decomposition, each definable closed subset A of Rⁿ is the zero-set of a function f:Rⁿ → R. This implies approximation of definable continuous functions and gluing of functions defined on closed definable sets.
Josef Vala (1993)
Mathematica Bohemica
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Some results in the geometry of four-parametric manifolds of three-dimensional spaces in the projective space are found. The properties of such a manifold with characteristics consisting of a quadric and two planes are studied. The properties of the manifold dual to are found. Some results in the geometry of linear spaces from [1],[2],[3],[4] are used. The notation of the quantities is the same as in [4].
A. Beltrán, M. Falla Luza, D. Marín (2014)
Annales de la faculté des sciences de Toulouse Mathématiques
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The aim of this work is to study global -webs with vanishing curvature. We wish to investigate degree foliations for which their dual web is flat. The main ingredient is the Legendre transform, which is an avatar of classical projective duality in the realm of differential equations. We find a characterization of degree foliations whose Legendre transform are webs with zero curvature.
Christine Vespa (2008)
Fundamenta Mathematicae
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We continue the study of the category of functors , associated to ₂-vector spaces equipped with a nondegenerate quadratic form, initiated in J. Pure Appl. Algebra 212 (2008) and Algebr. Geom. Topology 7 (2007). We define a filtration of the standard projective objects in ; this refines to give a decomposition into indecomposable factors of the first two standard projective objects in : and . As an application of these two decompositions, we give a complete description of the polynomial...
Qingying Bu, Gerard Buskes (2014)
Studia Mathematica
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Let E be a Banach space with 1-unconditional basis. Denote by (resp. ) the main diagonal space of the n-fold full (resp. symmetric) projective Banach space tensor product, and denote by (resp. ) the main diagonal space of the n-fold full (resp. symmetric) projective Banach lattice tensor product. We show that these four main diagonal spaces are pairwise isometrically isomorphic, and in addition, that they are isometrically lattice isomorphic to , the completion of the n-concavification...