## Abstract

Let {Φ_{i}}_{i=1}^{κ} be monotone maps on a hereditarily indecomposable continuum X. It is proved that the following are equivalent: (i) The product map Φ = (Φ_{1}, Φ_{2}, ..., Φ_{κ}) is light, (ii) Φ is an embedding. (iii) Each f in C(X, R) is representable as f = Σ_{i=1}^{κ}g_{i}oΦ_{i} with g_{i} ∈ C(Φ_{i}(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 R^{2}. In particular the n-dimensional B-coordinate projections have no stable values on X.

Original language | English |
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Pages (from-to) | 241-249 |

Number of pages | 9 |

Journal | Topology and its Applications |

Volume | 68 |

Issue number | 3 |

DOIs | |

State | Published - 1 Jan 1996 |

Externally published | Yes |

## Keywords

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

## ASJC Scopus subject areas

- Geometry and Topology