Monotone basic embeddings of hereditarily indecomposable continua

Let {ϑi}i = 1k be monotone maps on a hereditarily indecomposable continuum X. It is proved that the following are equivalent: 1. e product map ϑ = (ϑ1, ϑ2, …, ϑk) is light. is an embedding. Each ƒ in C(X, R) is representable as ƒ = ∑i = 1kgioϑi with ϑ ϵ C(ϑi(X), R). s applied to prove the following result which is related to the Chogoshvili conjecture: ⩾ 2 and let X be an n-dimensional hereditarily indecomposable continuum. X can be embedded in a separable Hilbert space H such that: 1. e restriction to X of the continuous linear functionals of H forms a dense subset of C(X, R). here 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. rticular the n-dimensional B-coordinate projections have no stable values on X.