A subspace of ℝ3 for which Cmp ≠ def

Michael Levin, Jack Segal

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We construct a separable metric space E in ℝ3 for which both the small and large compactness degrees cmp E = Cmp E = 1 and the compactness deficiency def E = 2. This improves on the example in ℝ4 given by R. Pol (1992) as a counterexample to the well-known conjecture of J. de Groot.

Original languageEnglish
Pages (from-to)165-168
Number of pages4
JournalTopology and its Applications
Issue number2
StatePublished - 1 Jan 1999
Externally publishedYes


  • Compactness deficiency
  • Compactness degree
  • De Groot's conjecture

ASJC Scopus subject areas

  • Geometry and Topology


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