Regular cylindrical algebraic decomposition

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We show that a strong well-based cylindrical algebraic decomposition P of a bounded semi-algebraic set S is a regular cell decomposition, in any dimension and independently of the method by which P is constructed. Being well-based is a global condition on P that holds for the output of many widely used algorithms. We also show the same for S of dimension at most 3 and P a strong cylindrical algebraic decomposition that is locally boundary simply connected: this is a purely local extra condition.

Original languageEnglish
Pages (from-to)43-59
Number of pages17
JournalJournal of the London Mathematical Society
Issue number1
Early online date29 Jul 2019
Publication statusPublished - 25 Feb 2020


  • 14P10 (primary)
  • 57N99
  • 68W30 (secondary)

ASJC Scopus subject areas

  • General Mathematics


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