A note on the predual of Lip(S, d)
J. A. Johnson (1979)
Colloquium Mathematicae
Similarity:
J. A. Johnson (1979)
Colloquium Mathematicae
Similarity:
Jeff Cheeger, Bruce Kleiner, Andrea Schioppa (2016)
Analysis and Geometry in Metric Spaces
Similarity:
We prove metric differentiation for differentiability spaces in the sense of Cheeger [10, 14, 27]. As corollarieswe give a new proof of one of the main results of [14], a proof that the Lip-lip constant of any Lip-lip space in the sense of Keith [27] is equal to 1, and new nonembeddability results.
P. Mankiewicz (1983)
Fundamenta Mathematicae
Similarity:
K. Leśniak (2007)
Bulletin of the Polish Academy of Sciences. Mathematics
Similarity:
The Lifshits theorem states that any k-uniformly Lipschitz map with a bounded orbit on a complete metric space X has a fixed point provided k < ϰ(X) where ϰ(X) is the so-called Lifshits constant of X. For many spaces we have ϰ(X) > 1. It is interesting whether we can use the Lifshits theorem in the theory of iterated function systems. Therefore we investigate the value of the Lifshits constant for several classes of hyperspaces.
Diethard Pallaschke, Dieter Pumplün (2015)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Similarity:
In this paper the universal properties of spaces of Lipschitz functions, defined over metric spaces, are investigated.
N. J. Kalton, G. Lancien (2008)
Fundamenta Mathematicae
Similarity:
We answer a question of Aharoni by showing that every separable metric space can be Lipschitz 2-embedded into c₀ and this result is sharp; this improves earlier estimates of Aharoni, Assouad and Pelant. We use our methods to examine the best constant for Lipschitz embeddings of the classical -spaces into c₀ and give other applications. We prove that if a Banach space embeds almost isometrically into c₀, then it embeds linearly almost isometrically into c₀. We also study Lipschitz embeddings...
Nigel J. Kalton (2008)
Revista Matemática Complutense
Similarity:
Jeremy T. Tyson (2005)
Fundamenta Mathematicae
Similarity:
We study the bi-Lipschitz embedding problem for metric compacta hyperspaces. We observe that the compacta hyperspace K(X) of any separable, uniformly disconnected metric space X admits a bi-Lipschitz embedding in ℓ². If X is a countable compact metric space containing at most n nonisolated points, there is a Lipschitz embedding of K(X) in ; in the presence of an additional convergence condition, this embedding may be chosen to be bi-Lipschitz. By way of contrast, the hyperspace K([0,1])...
Sophocles K. Mercourakis, Georgios Vassiliadis (2018)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
Immo Hahlomaa (2005)
Fundamenta Mathematicae
Similarity:
We show that pointwise bounds on the Menger curvature imply Lipschitz parametrization for general compact metric spaces. We also give some estimates on the optimal Lipschitz constants of the parametrizing maps for the metric spaces in Ω(ε), the class of bounded metric spaces E such that the maximum angle for every triple in E is at least π/2 + arcsinε. Finally, we extend Peter Jones's travelling salesman theorem to general metric spaces.
J. E. Valentine, S. G. Wayment (1973)
Colloquium Mathematicae
Similarity:
Zajíček, L.
Similarity:
Gilles Godefroy (2020)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
We show the existence of Lipschitz approximable separable spaces which fail Grothendieck's approximation property. This follows from the observation that any separable space with the metric compact approximation property is Lipschitz approximable. Some related results are spelled out.
Nigel J. Kalton (2004)
Collectanea Mathematica
Similarity:
We study the structure of Lipschitz and Hölder-type spaces and their preduals on general metric spaces, and give applications to the uniform structure of Banach spaces. In particular we resolve a problem of Weaver who asks wether if M is a compact metric space and 0 < α < 1, it is always true the space of Hölder continuous functions of class α is isomorphic to l. We show that, on the contrary, if M is a compact convex subset of a Hilbert space this isomorphism holds if...