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Showing 1 to 20 of 75 for “"Metric spaces"”.
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Boolean-valued probabilistic metric spaces
… closely resembling the theory of probabilistic metric spaces. In this development the complete Boolean algebra used must have the form of the quotient algebra of some atomless probability space ($\Omega,{\cal A},P$) modulo its class of null sets. In this setting the real numbers in the Boolean …
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Convexity in quasi-metric spaces
… an injective hull in the categories of T-quasi-metric spaces and of T-ultra-quasi-metric spaces with nonexpansive maps.
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Lipschitz Geometry of Banach and Metric Spaces
… about the isomorphic classification of Hilbert spaces.</p> <p> Next we will find bounds on the distortion of subsets of infinite dimensional Hilbert space. This concept compares the extrinsic straight line distance inherited from the underlying space to the path metric of a subset. We will then …
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partial translation algebras for certain discrete metric spaces
… analogue of the reduced group C*-algebra<br/>for metric spaces. Such an algebra is constructed from a partial translation<br/>structure, a structure which any bounded geometry uniformly discrete metric<br/>space admits; we prove that these structures restrict to subspaces and are<br/>preserved by …
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Algorithmic randomness on computable metric spaces and hyperspaces
… generalizing Martin-Löf randomness to computable metric spaces with arbitrary measure (for examples of this type of generalization see Gács [14], Rojas and Hoyrup [15]. The aim of this generalization is to define algorithmic randomness on the hyperspace of non-empty compact subsets of a computable …
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Hyperconvexity and endpoints in T₀-quasi-metric spaces
… made in the investigation of hyperconvexity in metric spaces. Recently Kemajou and others have published an article concerning hyperconvexity in T₀-quasi-metric spaces. In 1964 Isbell introduced and studied the concept of an endpoint of a metric space. The aim of this dissertation is to begin an …
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Hyperconvex hulls in catergories of quasi-metric spaces
Isbell showed that every metric space has an injective hull, that is, every metric space has a “minimal” hyperconvex metric superspace. Dress then showed that the hyperconvex hull is a tight extension. In analogy to Isbell’s theory Kemajou et al. proved that each T₀-quasi-metric space X has a …
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A quasi-pseudometrizability problem for ordered metric spaces
… results in the setting of ordered topological spaces related to the Hanai-Morita-Stone Theorem. The latter says that if f is a closed continuous map of a metric space X onto a topological space Y then the following statements are equivalent: (i) Y satisfies the first countability axiom; (ii) …
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Essays on Metric Spaces and Macro-Finance [védés előtt]
… where the reader could imagine a geometric shape (very similar to a geometric ball) with it’s important trigonometric angles, semi-convex functions, sequence of these functions and the associated gradient flows. Chapter 2. relies on the mathematical concepts and characteristics from …
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Coloring of Metric Spaces and L(2,1)-Labeling of Graphs
We also show that lambda(G) = q 2 + q = Delta2 - Delta for the incidence graph G of the projective plane PG (2, q). To prove this result, we convert the problem to a problem of packing of bipartite graphs into a complete bipartite graph. We also bound lambda(G) when G is the Kneser graph K(2k + 1, …
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Warped products of metric spaces of curvature bounded from above
… on smooth Riemannian manifolds, to geodesic metric spaces and prove the analogue of the theorems on spaces with curvature bounded from above.
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BiLipschitz embeddings and nonembeddings of metric spaces and related problems
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2020-08-25 without embargo terms
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Extremal Problems for Curves in Metric Spaces of Curvature Bounded Above
… problems involving curvature and curve length in metric spaces of curvature bounded above in the sense of Alexandrov. To a large extent, these problems have previously been solved only in Euclidean space. In addition to a nontrivial extention of the definition of total curvature, we give here …
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A Study of Concept Images and Concept Definitions related to Metric Spaces
… the concept images held by students concerning metric spaces. I was specifically interested in the concept of an open set in a metric space. This work also addresses the topics of distance and open balls, which are both essential when considering open sets. Also, I sought to investigate the …
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Rotations in Locally Bounded Linear Metric Spaces Which Are Not Locally Convex
Made available in DSpace on 2014-12-05T21:50:15Z (GMT). No. of bitstreams: 1 6001618.pdf: 1607424 bytes, checksum: e6216f96e0482f879ca9d56f5f047b1f (MD5) Previous issue date: 1960
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Geometry in metric spaces and fixed point theorems for classes of nonexpansive type mappings
… mappings in the general context of metric spaces. Additionally, our tech- niques will allow us to deduce the existence of common xed points for groups of such mappings based on features of the closed balls of the metric space. In order to do that, the concepts of normal structure and …
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A characterization of Bi-Lipschitz embeddable metric spaces in terms of local Bi-Lipschitz embeddability
… uniformly perfect, complete, doubling metric spaces which embed bi-Lipschitzly into Euclidean space. Our result applies in particular to spaces of Grushin type equipped with Carnot-Carath ́eodory distance. Hence we obtain the first example of a sub-Riemannian manifold admitting such a …
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New methods for fixed-margin binary matrix sampling, Fréchet covariance, and MANOVA tests for random objects in multiple metric spaces
… we explore is comparing random objects in metric spaces lacking a coordinate system. Traditional definitions of the mean and variance no longer apply, and standard statistical tests have needed reconceptualization in terms of only distances in the metric space. We consider the multivariate …
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Algorithmic embeddings
… results on low distortion mappings between metric spaces. An embedding between two metric spaces is a mapping between the two metric spaces and the distortion of the embedding is the factor by which the distances change. We have pioneered theoretical work on relative (or approximation) …
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Zero-dimensional spaces and their inverse limits
… we investigate zero-dimensional compact metric spaces and their inverse limits. We construct an uncountable family of zero-dimensional compact metric spaces homeomorphic to their Cartesian squares. It is known that the inverse limit on [0,1] with an upper semi-continuous function with a …
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