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manuscripta mathematica

, Volume 3, Issue 1, pp 1–5 | Cite as

On the connectedness of isomorphism classes

  • Robert A. McGuigan
Article
  • 20 Downloads

Abstract

This paper is concerned with some topological properties of a notion of distance between normed linear spaces which is due to Banach and Mazur [1], We are interested in a pseudometric space associated naturally with this notion of distance, and our main result is that this pseudometric space is always pathwise connected.

Keywords

Number Theory Linear Space Algebraic Geometry Topological Group Topological Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography

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    BANACH, S.: Théorie des Opérations Linéaires, p.242, New York, Chelsea, 1955.Google Scholar
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    DVORETSKY, A.: Some Results on Convex Bodies and Banach Spaces, Proc. Int. Symposium on Linear Spaces, held at the Hebrew Univ. of Jerusalem 1960, 123–160, Jerusalem, 1961.Google Scholar
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    GURARII, V.I.: Spaces of Universal Disposition, Isotropic Spaces, and the Mazur Problem on Rotations of Banach Spaces, Siberian Math. Journal 7, 799–807 (1966).Google Scholar
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    MCGUIGAN, R.A.: Near Isometry of Banach Spaces and the Banach-Mazur Distance, Ph.D. thesis, Univ. of Maryland, 1968.Google Scholar
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    SCHAFFER, J.J.: Inner Diameter, Perimeter, and Girth of Spheres, Math. Ann. 173, 59–82 (1967).Google Scholar
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    WHITLEY, R.: The Size of the Unit Sphere, Can. J. Math. 20, 450–455 (1968).Google Scholar

Copyright information

© Springer-Verlag 1970

Authors and Affiliations

  • Robert A. McGuigan
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of MassachusettsAmherst

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