Certain 2-stable embeddings

Tadeusz Dobrowolski, Michael Levin, Leonard R. Rubin

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


The Chogoshvili Claim states that for each k-dimensional compactum X in ℝn, there exists an (n - k)-plane P in ℝn such that X is not removable from P. This means that for some ε > 0, every map f : X → ℝn with ∥x - f(x)∥ < ε for all x ∈ X, has the property that f(X) ∩ P ≠ Ø. A counterexample to this claim has recently been constructed by A. Dranishnikov. Our results show, among other things, that each 2-dimensional LC1 compactum, and hence each 2-dimensional disk, obeys the claim. To help indicate the sharpness of the preceding, we also provide a local path-connectification of Dranishnikov's example.

Original languageEnglish
Pages (from-to)81-90
Number of pages10
JournalTopology and its Applications
Issue number1-2
StatePublished - 1 Jan 1997
Externally publishedYes


  • ANR
  • Chogoshvili's Claim
  • LC-spaces
  • Unicoherent locally connected continua

ASJC Scopus subject areas

  • Geometry and Topology


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