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Distances between Banach spaces
Abstract The main object of the paper is to study the distance between Banach spaces introduced by Kadets. For Banach spaces X and Y, the Kadets distance is defined to be the infimum of the HausdorffExpand
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Minimum congestion spanning trees of grids and discrete toruses
TLDR
The paper is devoted to estimates of the spanning tree congestion for grid graphs and discrete toruses of dimensions two and three. Expand
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Metric dimensions of minor excluded graphs and minor exclusion in groups
TLDR
We prove that minor excluded graphs have finite Assouad-Nagata dimension and study minor exclusion for Cayley graphs of finitely generated groups. Expand
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Embeddability of locally finite metric spaces into Banach spaces is finitely determined
The main purpose of the paper is to prove the following results: • Let A be a locally finite metric space whose finite subsets admit uniformly bilipschitz embeddings into a Banach space X. Then AExpand
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Topologies on the set of all subspaces of a banach space and related questions of banach space geometry
Abstract The survey is devoted to two of the most common topologies on the set of all subspaces of a Banach space. The first part contains definitions of the topologies and a description of theirExpand
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Minimum congestion spanning trees in planar graphs
  • M. Ostrovskii
  • Mathematics, Computer Science
  • Discret. Math.
  • 22 September 2009
TLDR
The main purpose of the paper is to develop an approach to the evaluation or the estimation of the spanning tree congestion of planar graphs. Expand
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Sobolev spaces on graphs
The present paper is devoted to discrete analogues of Sobolev spaces of smooth functions. The discrete analogues that we consider are spaces of functions on vertex sets of graphs. Such spaces haveExpand
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Expansion properties of metric spaces not admitting a coarse embedding into a Hilbert space
The main purpose of the paper is to find some expansion properties of locally finite metric spaces which do not embed coarsely into a Hilbert space. The obtained result is used to show that infiniteExpand
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Extremal Problems for Operators in Banach Spaces Arising in the Study of Linear Operator Pencils
Abstract.Inspired by some problems on fractional linear transformations the authors introduce and study the class of operators satisfying the condition $$\left\| A \right\| = \max \{ \rhoExpand
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Weak closures and derived sets in dual Banach spaces
The main results of the paper: \textbf{(1)} The dual Banach space contains a linear subspace such that the set of all limits of weak convergent bounded nets in is a proper norm-dense subset of if andExpand
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