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Analysis and Geometry in Metric Spaces

Ed. by Ritoré, Manuel


CiteScore 2017: 0.65

SCImago Journal Rank (SJR) 2017: 1.063
Source Normalized Impact per Paper (SNIP) 2017: 0.833

Mathematical Citation Quotient (MCQ) 2017: 0.86

Open Access
Online
ISSN
2299-3274
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Uniformly Convex Metric Spaces

Martin Kell
Published Online: 2014-12-10 | DOI: https://doi.org/10.2478/agms-2014-0015

Abstract

In this paper the theory of uniformly convex metric spaces is developed. These spaces exhibit a generalized convexity of the metric from a fixed point. Using a (nearly) uniform convexity property a simple proof of reflexivity is presented and a weak topology of such spaces is analyzed. This topology, called coconvex topology, agrees with the usually weak topology in Banach spaces. An example of a CAT(0)-space with weak topology which is not Hausdorff is given. In the end existence and uniqueness of generalized barycenters is shown, an application to isometric group actions is given and a Banach-Saks property is proved.

Keywords: convex metric spaces; weak topologies; generalized barycenters; Banach-Saks property;

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About the article

Received: 2014-07-07

Accepted: 2014-11-14

Published Online: 2014-12-10


Citation Information: Analysis and Geometry in Metric Spaces, Volume 2, Issue 1, ISSN (Online) 2299-3274, DOI: https://doi.org/10.2478/agms-2014-0015.

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© 2014 Martin Kell. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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