Order-two continuous Hausdorff images of compact ordinals (Q797173)

The author proves the following surprising result: A Hausdorff space is homeomorphic to a compact scattered ordered space iff it is an order-two image of a compact ordinal. In fact, the implication (\(\Rightarrow)\) was proved in an earlier paper [see the review above] and it was shown that an order-two \(T_ 2\)-image of a scattered compact ordered space need not be orderable. The implication (\(\Leftarrow)\) follows from the following: Each order-two \(T_ 2\)-image of a compact well ordered space is orderable. This theorem is proved by a very careful analysis of the structure of the space and the map under above assumptions.