Related papers: Discrete Morrey spaces and their generalizations
Characterizations of paracompact finite $C$-spaces via continuous selections are given. We apply these results to obtain some properties of finite $C$-spaces. Factorization theorems and a completion theorem for finite $C$- spaces are also…
The space of smooth curves admits a beautiful compactification by the moduli space of Deligne-Mumford stable curves. In this paper, we undertake a systematic investigation of alternate modular compactifications of the space of smooth…
The paper is devoted to a categorical study of the category of probabilistic metric spaces. The study is based on an isomorphic description of the category of probabilistic metric spaces. The isomorphic description was obtained in [3] and…
This article provides an overview of various notions of shape spaces, including the space of parametrized and unparametrized curves, the space of immersions, the diffeomorphism group and the space of Riemannian metrics. We discuss the…
Some sharp discrete inequalities in normed linear spaces are obtained. New reverses of the generalised triangle inequality are also given.
A condition for the presence of a "gap" between symmetric spaces sufficient for the inclusion of one of these spaces into the other to be disjointly strictly singular is found. This condition is stated in terms of fundamental functions of…
We introduce self-similar algebras and groups closely related to the Thue-Morse sequence, and begin their investigation by describing a character on them, the "spread" character.
Open discrete mappings with a modulus condition in metric spaces are considered. Some results related to local behavior of mappings as well as theorems about continuous extension to a boundary are proved.
We develop a unified framework for the study of properties involving diagonalizations of dense families in topological spaces. We provide complete classification of these properties. Our classification draws upon a large number of methods…
As a generalization of singular linear spaces, we introduce the concept of t-singular linear spaces, make some anzahl formulas of subspaces, and determine the suborbits of t-singular linear groups.
We generalize a theorem of Delzant classifying compact connected symplectic manifolds with completely integrable torus actions to certain singular symplectic spaces. The assumption on singularities is that if they are not finite quotient…
We characterize 1-complemented subspaces of finite codimension in strictly monotone one-$p$-convex, $2<p<\infty,$ sequence spaces. Next we describe, up to isometric isomorphism, all possible types of 1-unconditional structures in sequence…
This work is concerned with the quantification of the epistemic uncertainties induced the discretization of partial differential equations. Following the paradigm of probabilistic numerics, we quantify this uncertainty probabilistically.…
We characterize rotund, uniformly rotund, locally uniformly rotund and compactly locally uniformly rotund spaces in terms of sets of (almost) farthest points from the unit sphere using the generalized diameter. For this we introduce few…
We consider the global Morrey-type spaces with variable exponents and general function defining these spaces. In the case of unbounded sets, we prove boundedness of the Hardy-Littlewood maximal operator, potential type operator in these…
We investigate a tangent space at a point of a general metric space and metric space valued derivatives. The conditions under which two different subspace of a metric space have isometric tangent spaces in a common point of these subspaces…
We consider the global symplectic classification problem of plane curves. First we give the exact classification result under symplectomorphisms, for the case of generic plane curves, namely immersions with transverse self-intersections.…
We give a characterization of smooth quadrics in terms of the existence of full exceptional collections of certain type, which generalizes a result of C.Vial for projective spaces.
In this paper we introduce the notions of statistical convergence and statistical Cauchyness of sequences in a metric-like space. We study some basic properties of these notions
We study the statistical convergence of metric valued sequences and of their subsequences. The interplay between the statistical and usual convergences in metric spaces is also studied.