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Published online by Cambridge University Press: 18 May 2009
In an earlier paper [5] we introduced the idea of an immersion f: Mm-ℝn with totally reducible focal set. Such an immersion has the property that, for all p ∈ M, the focal set with base p is a union of hyperplanes in the normal plane to f(M) at f(p). Trivially, this always holds if n = m + 1 so we only consider n > m + 1.