Monotone basic embeddings of hereditarily indecomposable continua

Michael Levin, Yaki Sternfeld

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Let {Φi}i=1κ be monotone maps on a hereditarily indecomposable continuum X. It is proved that the following are equivalent: (i) The product map Φ = (Φ1, Φ2, ..., Φκ) is light, (ii) Φ is an embedding. (iii) Each f in C(X, R) is representable as f = Σi=1κgii with gi ∈ C(Φi(X), R). This is applied to prove the following result which is related to the Chogoshvili conjecture: Let n ≥ 2 and let X be an n-dimensional hereditarily indecomposable continuum. X can be embedded in a separable Hilbert space H such that: (i) The restriction to X of the continuous linear functionals of H forms a dense subset of C(X, R). (ii) There exists an orthonormal basis B for H such that the restriction to X of each 2-dimensional B-coordinate projection of H factors through some 1-dimensional space and as a result has no stable values in R2. In particular the n-dimensional B-coordinate projections have no stable values on X.

Original languageEnglish
Pages (from-to)241-249
Number of pages9
JournalTopology and its Applications
Issue number3
StatePublished - 1 Jan 1996
Externally publishedYes


  • Basic embeddings
  • Chogoshvili's conjecture
  • Hereditarily indecomposable continua
  • Monotone maps

ASJC Scopus subject areas

  • Geometry and Topology


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