Cleavability and scattered sets of non-trivial fibers
Abstract
In this paper, 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.
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