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Displaying similar documents to “On definably proper maps”

A theorem on generic intersections in an o-minimal structure

Krzysztof Jan Nowak (2014)

Fundamenta Mathematicae

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Consider a transitive definable action of a Lie group G on a definable manifold M. Given two (locally) definable subsets A and B of M, we prove that the dimension of the intersection σ(A) ∩ B is not greater than the expected one for a generic σ ∈ G.

A decomposition of a set definable in an o-minimal structure into perfectly situated sets

Wiesław Pawłucki (2002)

Annales Polonici Mathematici

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A definable subset of a Euclidean space X is called perfectly situated if it can be represented in some linear system of coordinates as a finite union of (graphs of) definable 𝓒¹-maps with bounded derivatives. Two subsets of X are called simply separated if they satisfy the Łojasiewicz inequality with exponent 1. We show that every closed definable subset of X of dimension k can be decomposed into a finite family of closed definable subsets each of which is perfectly situated and such...

On minimal Hausdorff and minimal Urysohn functions

Filippo Cammaroto, Andrei Catalioto, Jack Porter (2011)

Open Mathematics

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In this article, we extend the work on minimal Hausdorff functions initiated by Cammaroto, Fedorchuk and Porter in a 1998 paper. Also, minimal Urysohn functions are introduced and developed. The properties of heredity and productivity are examined and developed for both minimal Hausdorff and minimal Urysohn functions.

Two commuting maps without common minimal points

Tomasz Downarowicz (2011)

Colloquium Mathematicae

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We construct an example of two commuting homeomorphisms S, T of a compact metric space X such that the union of all minimal sets for S is disjoint from the union of all minimal sets for T. In other words, there are no common minimal points. This answers negatively a question posed in [C-L]. We remark that Furstenberg proved the existence of "doubly recurrent" points (see [F]). Not only are these points recurrent under both S and T, but they recur along the same sequence of powers. Our...

A first-order version of Pfaffian closure

Sergio Fratarcangeli (2008)

Fundamenta Mathematicae

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The purpose of this paper is to extend a theorem of Speissegger [J. Reine Angew. Math. 508 (1999)], which states that the Pfaffian closure of an o-minimal expansion of the real field is o-minimal. Specifically, we display a collection of properties possessed by the real numbers that suffices for a version of the proof of this theorem to go through. The degree of flexibility revealed in this study permits the use of certain model-theoretic arguments for the first time, e.g. the compactness...

Minimal resolutions and other minimal models.

Agustí Roig (1993)

Publicacions Matemàtiques

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In many situations, minimal models are used as representatives of homotopy types. In this paper we state this fact as an equivalence of categories. This equivalence follows from an axiomatic definition of minimal objects. We see that this definition includes examples such as minimal resolutions of Eilenberg-Nakayama-Tate, minimal fiber spaces of Kan and Λ-minimal Λ-extensions of Halperin. For the first one, this is done by generalizing the construction of minimal resolutions of modules...

Minimal Niven numbers

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

Acta Arithmetica

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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.

Noninvertible minimal maps

Sergiĭ Kolyada, L'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...