Embedding in Dugundji spaces, with an application to linear topological classification of spaces of continuous functions
A subspace A of a topological space X is said to be -embedded ((point-finite)-embedded) in X if every (point-finite) partition of unity α on A with |α| ≤ γ extends to a (point-finite) partition of unity on X. The main results are: (Theorem A) A subspace A of X is (point-finite)-embedded in X iff it is -embedded and every countable intersection B of cozero-sets in X with B ∩ A = ∅ can be separated from A by a cozero-set in X. (Theorem B) The product A × [0,1] is (point-finite)-embedded in X...