On Finite-dimensional Maps Ii H. Murat Tuncali and Vesko Valov

Let f : X → Y be a perfect n-dimensional surjective map of paracompact spaces and Y a C-space. We consider the following property of continuous maps g : X → Ik = [0, 1], where 1 ≤ k ≤ ω: each g(f(y)), y ∈ Y , is at most n-dimensional. It is shown that all maps g ∈ C(X, In+1) with the above property form a dense Gδ-set in the function space C(X, I n+1 ) equipped with the source limitation topology. Moreover, for every n + 1 ≤ m ≤ ω the space C(X, Im) contains a dense Gδ-set of maps having this property.