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Archiv der Mathematik

, Volume 110, Issue 1, pp 53–59 | Cite as

Game-theoretic characterization of the Gurarii space

  • Wiesław KubiśEmail author
Open Access
Article

Abstract

We present a simple and natural infinite game building an increasing chain of finite-dimensional Banach spaces. We show that one of the players has a strategy with the property that, no matter how the other player plays, the completion of the union of the chain is linearly isometric to the Gurariĭ space.

Keywords

Normed space Banach–Mazur game Gurariĭ space Eve 

Mathematics Subject Classification

46B04 46B06 46B25 

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Copyright information

© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Institute of MathematicsCzech Academy of SciencesPragueCzechia
  2. 2.Faculty of Natural Sciences, College of ScienceCardinal Stefan Wyszyński UniversityWarsawPoland

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