Cleavability over scattered first-countable LOTS

In this paper we will show that if X is a compactum cleavable over a first-countable scattered linearly ordered topological space (LOTS) Y, then X does not have to be homeomorphic to a subspace of Y. We will then discover the conditions under which cleavability implies a homeomorphism exists. Furthermore, we will show that if X is a compactum cleavable over a first-countable LOTS, then X is a LOTS.