Forcing relation on minimal interval patterns

Jozef Bobok

Displaying similar documents to “Forcing relation on minimal interval patterns”

Noninvertible minimal maps

Sergiĭ Kolyada, L&#039;ubomír Snoha, Sergeĭ Trofimchuk (2001)

Fundamenta Mathematicae

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For a discrete dynamical system given by a compact Hausdorff space X and a continuous selfmap f of X the connection between minimality, invertibility and openness of f is investigated. It is shown that any minimal map is feebly open, i.e., sends open sets to sets with nonempty interiors (and if it is open then it is a homeomorphism). Further, it is shown that if f is minimal and A ⊆ X then both f(A) and $f^{- 1} (A)$ share with A those topological properties which describe how large a set is. Using...

Uniqueness of minimal projections onto two-dimensional subspaces

Boris Shekhtman, Lesław Skrzypek (2005)

Studia Mathematica

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We prove that minimal projections from $L_{p}$ (1 < p < ∞) onto any two-dimensional subspace are unique. This result complements the theorems of W. Odyniec ([OL, Theorem I.1.3], [O3]). We also investigate the minimal number of norming points for such projections.

Cylinder cocycle extensions of minimal rotations on monothetic groups

Mieczysław K. Mentzen, Artur Siemaszko (2004)

Colloquium Mathematicae

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The main results of this paper are: 1. No topologically transitive cocycle $ℝ^{m}$ -extension of minimal rotation on the unit circle by a continuous real-valued bounded variation ℤ-cocycle admits minimal subsets. 2. A minimal rotation on a compact metric monothetic group does not admit a topologically transitive real-valued cocycle if and only if the group is finite.

Induced subsystems associated to a Cantor minimal system

Heidi Dahl, Mats Molberg (2009)

Colloquium Mathematicae

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Let (X,T) be a Cantor minimal system and let (R,) be the associated étale equivalence relation (the orbit equivalence relation). We show that for an arbitrary Cantor minimal system (Y,S) there exists a closed subset Z of X such that (Y,S) is conjugate to the subsystem (Z,T̃), where T̃ is the induced map on Z from T. We explore when we may choose Z to be a T-regular and/or a T-thin set, and we relate T-regularity of a set to R-étaleness. The latter concept plays an important role in the...

Density of Morse functions on sets definable in o-minimal structures

Ta Lê Loi (2006)

Annales Polonici Mathematici

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We present a tameness property of sets definable in o-minimal structures by showing that Morse functions on a definable closed set form a dense and open subset in the space of definable $C^{p}$ functions endowed with the Whitney topology.

Constants of strong uniqueness of minimal norm-one projections

A. Micek (2011)

Banach Center Publications

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In this paper we calculate the constants of strong uniqueness of minimal norm-one projections on subspaces of codimension k in the space $l_{\infty}^{(n)}$ . This generalizes a main result of W. Odyniec and M. P. Prophet [J. Approx. Theory 145 (2007), 111-121]. We applied in our proof Kolmogorov’s type theorem (see A. Wójcik [Approximation and Function Spaces (Gdańsk, 1979), PWN, Warszawa / North-Holland, Amsterdam, 1981, 854-866]) for strongly unique best approximation.

$C^{1}$ -minimal subsets of the circle

Dusa McDuff (1981)

Annales de l'institut Fourier

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Necessary conditions are found for a Cantor subset of the circle to be minimal for some $C^{1}$ -diffeomorphism. These conditions are not satisfied by the usual ternary Cantor set.

Codimension one minimal projections in Banach spaces and a mathematical programming problem

Vladimir P. Odinec

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CONTENTSIntroduction.........................................................................................................5§1. Notation and preliminaries............................................................................6§2. Mathematical Programming Problem related to minimal projections.............8§3. Criteria for uniqueness of minimal projections in $l_{1}^{m}$ ..........................16References......................................................................................................27 ...

A characterization of a minimal submanifold in $R^{n + p}$

Themis Koufogiorgos (1983)

Annales Polonici Mathematici

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O-minimal version of Whitney's extension theorem

Krzysztof Kurdyka, Wiesław Pawłucki (2014)

Studia Mathematica

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This is a generalized and improved version of our earlier article [Studia Math. 124 (1997)] on the Whitney extension theorem for subanalytic $^{p}$ -Whitney fields (with p finite). In this new version we consider Whitney fields definable in an arbitrary o-minimal structure on any real closed field R and obtain an extension which is a $^{p}$ -function definable in the same o-minimal structure. The Whitney fields that we consider are defined on any locally closed definable subset of Rⁿ. In such a...

On the minimal overlap problem of Erdös

L Moser (1959)

Acta Arithmetica

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A note on minimal zero-sum sequences over ℤ

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 $a ₁, . . ., a_{h}$ and negative terms $b ₁, . . ., b_{k}$ . We prove that h ≤ ⌊σ⁺/k⌋ and k ≤ ⌊σ⁺/h⌋, where $σ ⁺ = \sum_{i = 1}^{h} a_{i} = - \sum_{j = 1}^{k} b_{j}$ . 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...

On gradients of functions definable in o-minimal structures

Krzysztof Kurdyka (1998)

Annales de l'institut Fourier

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We prove the o-minimal generalization of the Łojasiewicz inequality $∥ grad f ∥ \geq | f |^{α}$ , with $α < 1$ , in a neighborhood of $a$ , where $f$ is real analytic at $a$ and $f (a) = 0$ . We deduce, as in the analytic case, that trajectories of the gradient of a function definable in an o-minimal structure are of uniformly bounded length. We obtain also that the gradient flow gives a retraction onto levels of such functions.

Minimal Niven numbers

H. Fredricksen, E. J. Ionascu, F. Luca, P. Stănică (2008)

Acta Arithmetica

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A note on universal minimal dynamical systems

Sławomir Turek (1991)

Commentationes Mathematicae Universitatis Carolinae

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Let $M (G)$ denote the phase space of the universal minimal dynamical system for a group $G$ . Our aim is to show that $M (G)$ is homeomorphic to the absolute of $D^{2^{ω}}$ , whenever $G$ is a countable Abelian group.

Minimal rankings of the Cartesian product Kₙ ☐ Kₘ

Gilbert Eyabi, Jobby Jacob, Renu C. Laskar, Darren A. Narayan, Dan Pillone (2012)

Discussiones Mathematicae Graph Theory

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For a graph G = (V, E), a function f:V(G) → 1,2, ...,k is a k-ranking if f(u) = f(v) implies that every u - v path contains a vertex w such that f(w) > f(u). A k-ranking is minimal if decreasing any label violates the definition of ranking. The arank number, $ψ_{r} (G)$ , of G is the maximum value of k such that G has a minimal k-ranking. We completely determine the arank number of the Cartesian product Kₙ ☐ Kₙ, and we investigate the arank number of Kₙ ☐ Kₘ where n > m.

Weierstrass division theorem in definable $C^{\infty}$ germs in a polynomially bounded o-minimal structure

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 $C^{\infty}$ functions.