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1 results

  • 11 - Effros’ Theorem and the Cornerstone Theorems of Functional Analysis

  • N. H. Bingham, Imperial College London, Adam J. Ostaszewski, London School of Economics and Political Science
  • Book:
    Category and Measure
    Published online:
    14 January 2025
    Print publication:
    23 January 2025, pp 172-183

  • Summary

    The Open Mapping Theorem – that a surjective continuous linear map between Fréchet spaces is open – is one of the cornerstones of linear functional analysis. Effros’ Theorem is a group-action counterpart: a continuous transitive action by a Polish group G on a non-meagre space X is open (i.e. point-evaluation maps $g \mapsto gx$ are open). We discuss action, micro-transitivity and shift-compactness. We investigate what we call the crimping property (arising in Banach’s classic book of 1932). It turns out that this is equivalent to the Effros property. Various related results are proved.