S. Levine Cleavability and linear orderability
In this talk, we provide a partial answer to a problem posed by A.
V.Arhangel'skii; we show that if X is a compactum cleavable over a separable
linearly ordered topological space (LOTS) Y such that for some continuous
function f from X to Y, the set of points on which f is not injective is
scattered, then X is a LOTS.