Rendiconti di Matematica e delle Sue Applicazioni (Sep 1994)
Developable spaces and cleavability
Abstract
If P is a class of topological spaces, then a topological space X is said to be cleavable over P if for every A ⊂ X there are a space Y ∈ P and a continuous mapping f : X → Y such that f(X) = Y and f −1f(A) = A. The space X is called divisible if for every A ⊂ X there exists a countable collection S of closed subsets of X such that for every x ∈ A and every y /∈ A there is a member S in S with x ∈ S and y /∈ S. We investigate cleavability over the class of (second countable) developable spaces and some relations between that cleavability and divisibility.
