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We propose a new concept of generalized differentiation of set-valued maps that captures the first order information. This concept encompasses the standard notions of Frechet differentiability, strict differentiability, calmness and…
We propose a new approach for metric learning by framing it as learning a sparse combination of locally discriminative metrics that are inexpensive to generate from the training data. This flexible framework allows us to naturally derive…
Geometric properties of schemes obtained by gluing algebras of monoids, including separation and finiteness properties, irreducibility, normality, catenarity, dimension, and Serre's properties (S_k) and (R_k), are investigated. This is used…
We introduce the notion of (almost isometric) local retracts in metric space as a natural non-linear version of the concepts of locally complemented and almost isometric ideals from Banach spaces. We prove that given two metric spaces…
Using approximations, we give several characterizations of separability of bimodules. We also discuss how separability properties can be used to transfer some representation theoretic properties from one ring to another one: contravariant…
We develop the theory of adequate moduli spaces in characteristic $p$ (and mixed characteristic) characterizing quotients by geometrically reductive group schemes.
In this paper we study fundamental directional properties of sets under the assumption of condition (SSP) (introduced in a previous paper). We show several transversality theorems in the singular case and an (SSP)-structure preserving…
In generalized Lebesgue spaces L^{p(.)} with variable exponent p(.) defined on the real axis, we obtain several inequalities of approximation by integral functions of finite degree. Approximation properties of Bernstein singular integrals…
In this paper we examine various properties/constructions which are known for reductive groups and we do some experiments to see to what extent they generalize to symmetric spaces.
In this paper, the Lipschitz clustering property of a metric space refers to the existence of Lipschitz retractions between its finite subset spaces. Obstructions to this property can be either topological or geometric features of the…
We construct a complete metric space $M$ of cardinality continuum such that every non-singleton closed separable subset of $M$ fails to be a Lipschitz retract of $M$. This provides a metric analogue to the various classical and recent…
The aim of this paper to introduce the reader to a recent point of view on the Lipschitz classifications of complex singularities. It presents the complete classification of Lipschitz geometry of complex plane curves singularities and in…
Continuing the analysis in a unified scheme for treating generalized superselection sectors based upon the notion of selection criteria for states of relevance in quantum physics, we extend the Doplicher-Roberts superselection theory for…
One goal of geometric measure theory is to understand how measures in the plane or higher dimensional Euclidean space interact with families of lower dimensional sets. An important dichotomy arises between the class of rectifiable measures,…
We make a systematic study of frames for metric spaces. We prove that every separable metric space admits a metric $\mathcal{M}_d$-frame. Through Lipschitz-free Banach spaces we show that there is a correspondence between frames for metric…
We use Fra\" iss\'e theoretic methods to construct several universal and ultrahomogeneous Polish metric structures. Namely, universal and ultrahomogeneous Polish metric space equipped with countably many closed subsets of its powers,…
The aim of this paper is to introduce new statistical criterions for estimation, suitable for inference in models with common continuous support. This proposal is in the direct line of a renewed interest for divergence based inference tools…
For Lipschitz maps between a metric measure space and a metric space, combining the ideas of Kirchheim's metric differentiability and Cheeger's differentiable structures leads to a Rademacher-type theorem for a notion of metric…
The Urysohn space is a separable complete metric space with two fundamental properties: (a) universality: every separable metric space can be isometrically embedded in it; (b) ultrahomogeneity: every finite isometry between two finite…
We prove a separable reduction theorem for sigma-porosity of Suslin sets. In particular, if A is a Suslin subset in a Banach space X, then each separable subspace of X can be enlarged to a separable subspace V such that A is sigma-porous in…