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Abstract

In this § and the next one, K will be a p-field, commutative or not. We shall mostly discuss only left vector-spaces over K; everything will apply in an obvious way to right vector-spaces. Only vector-spaces of finite dimension will occur; it is understood that these are always provided with their “natural topology” according to corollary 1 of th. 3, Chap. I-2. By th. 3 of Chap. I–2, every subspace of such a space V is closed in V. Taking coordinates, one sees that all linear mappings of such spaces into one another are continuous ; in particular, linear forms are continuous. Similarly, every injective linear mapping of such a space V into another is an isomorphism of V onto its image. As K is not compact, no subspace of V can be compact, except {0}.

Keywords

Local Field Haar Measure Closed Subgroup Discrete Subgroup Finite Dimension 
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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Copyright information

© Springer-Verlag Berlin · Heidelberg 1967

Authors and Affiliations

  • André Weil
    • 1
  1. 1.The Institute for Advanced StudyPrincetonUSA

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