On the tangency of sets in generalized metric spaces for certain functions of the class
T. Konik (1991)
Matematički Vesnik
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T. Konik (1991)
Matematički Vesnik
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Vincent Colin, Sheila Sandon (2015)
Journal of the European Mathematical Society
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We define an integer-valued non-degenerate bi-invariant metric (the discriminant metric) on the universal cover of the identity component of the contactomorphism group of any contact manifold. This metric has a very simple geometric definition, based on the notion of discriminant points of contactomorphisms. Using generating functions we prove that the discriminant metric is unbounded for the standard contact structures on and . On the other hand we also show by elementary arguments...
Stefan Neuwirth (1998)
Studia Mathematica
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We investigate several aspects of almost 1-unconditionality. We characterize the metric unconditional approximation property (umap) in terms of “block unconditionality”. Then we focus on translation invariant subspaces and of functions on the circle and express block unconditionality as arithmetical conditions on E. Our work shows that the spaces , p an even integer, have a singular behaviour from the almost isometric point of view: property (umap) does not interpolate between ...
Philippe Clément, Wolfgang Desch (2008)
Studia Mathematica
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Let , be complete separable metric spaces. Denote by (X) the space of probability measures on X, by the p-Wasserstein metric with some p ∈ [1,∞), and by the space of probability measures on X with finite Wasserstein distance from any point measure. Let , , be a Borel map such that f is a contraction from into . Let ν₁,ν₂ be probability measures on Ω with finite. On X we consider the subordinated measures . Then . As an application we show that the solution measures ...
Ivan Lončar (2017)
Archivum Mathematicum
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For metrizable continua, there exists the well-known notion of a Whitney map. If is a nonempty, compact, and metric space, then any Whitney map for any closed subset of can be extended to a Whitney map for [3, 16.10 Theorem]. The main purpose of this paper is to prove some generalizations of this theorem.
Nijjwal Karak (2017)
Czechoslovak Mathematical Journal
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In many recent articles, medians have been used as a replacement of integral averages when the function fails to be locally integrable. A point in a metric measure space is called a generalized Lebesgue point of a measurable function if the medians of over the balls converge to when converges to . We know that almost every point of a measurable, almost everywhere finite function is a generalized Lebesgue point and the same is true for every point of a continuous function....
Neil Seshadri (2009)
Bulletin de la Société Mathématique de France
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To any smooth compact manifold endowed with a contact structure and partially integrable almost CR structure , we prove the existence and uniqueness, modulo high-order error terms and diffeomorphism action, of an approximately Einstein ACH (asymptotically complex hyperbolic) metric on . We consider the asymptotic expansion, in powers of a special defining function, of the volume of with respect to and prove that the log term coefficient is independent of (and any choice...
Olli Tapiola (2016)
Colloquium Mathematicae
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With the help of recent adjacent dyadic constructions by Hytönen and the author, we give an alternative proof of results of Lechner, Müller and Passenbrunner about the -boundedness of shift operators acting on functions where 1 < p < ∞, X is a metric space and E is a UMD space.
Taras Banakh, Vesko Valov
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General position properties play a crucial role in geometric and infinite-dimensional topologies. Often such properties provide convenient tools for establishing various universality results. One of well-known general position properties is DDⁿ, the property of disjoint n-cells. Each Polish -space X possessing DDⁿ contains a topological copy of each n-dimensional compact metric space. This fact implies, in particular, the classical Lefschetz-Menger-Nöbeling-Pontryagin-Tolstova embedding...
Naotsugu Chinen (2015)
Commentationes Mathematicae Universitatis Carolinae
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By , , we denote the -th symmetric product of a metric space as the space of the non-empty finite subsets of with at most elements endowed with the Hausdorff metric . In this paper we shall describe that every isometry from the -th symmetric product into itself is induced by some isometry from into itself, where is either the Euclidean space or the sphere with the usual metrics. Moreover, we study the -th symmetric product of the Euclidean space up to bi-Lipschitz equivalence...
Muhammad Arshad, Eskandar Ameer, Aftab Hussain (2015)
Archivum Mathematicum
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The aim of this paper is to introduce some new fixed point results of Hardy-Rogers-type for ---contraction in a complete metric space. We extend the concept of -contraction into an ---contraction of Hardy-Rogers-type. An example has been constructed to demonstrate the novelty of our results.
Jan Kurek, Włodzimierz Mikulski (2014)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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If is a Riemannian manifold, we have the well-known base preserving vector bundle isomorphism given by between the tangent and the cotangent bundles of . In the present note, we generalize this isomorphism to the one between the -th order vector tangent and the -th order cotangent bundles of . Next, we describe all base preserving vector bundle maps depending on a Riemannian metric in terms of natural (in ) tensor fields on .
Wojciech Zygmunt (2016)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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In this note we shall prove that for a continuous function , where , the paratingent of at is a non-empty and compact set in if and only if satisfies Lipschitz condition in a neighbourhood of . Moreover, in this case the paratingent is a connected set.
Richard J. Gardner, Daniel Hug, Wolfgang Weil (2013)
Journal of the European Mathematical Society
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An investigation is launched into the fundamental characteristics of operations on and between sets, with a focus on compact convex sets and star sets (compact sets star-shaped with respect to the origin) in -dimensional Euclidean space . It is proved that if , with three trivial exceptions, an operation between origin-symmetric compact convex sets is continuous in the Hausdorff metric, covariant, and associative if and only if it is addition for some . It is also demonstrated...