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  • 4 - Infinite Combinatorics in Rn: Shift-Compactness

  • 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 71-77

  • Summary

    The importance of infinite combinatorics is indicated by the book’s subtitle. Category (and indeed measure) methods are particularly useful for establishing generic behaviour: showing that a particular property predominates, without needing to (or indeed, being able to) show any specific example. Results of this type proved here include the Generic Dichotomy Principle, Generic Completeness Principle, Kestelman–Borwein–Ditor Shift-Compactness Theorem (used many times and abbreviated to KBD) and Kemperman’s Displacement Theorem.