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Compact, separable, linearly ordered spaces. (English) Zbl 0889.54014

A well-known question on monotonically normal spaces is whether each compact such space is the continuous image of a compact ordered space. This paper provides an affirmative answer for separable zero-dimensional spaces. The proof is a combinatorial and topological tour de force.
In the meantime the author has improved the result, first by removing the assumption of zero-dimensionality [Zero-dimensionality and monotone normality, Topology Appl. 85, 319-333 (1998)] and more recently by relaxing separability to first-countability [Compact first countable linearly ordered spaces, http://www.unipissing.ca/topology/v/a/a/a/14.htm].
Reviewer: K.P.Hart (Delft)

MSC:

54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
54A35 Consistency and independence results in general topology
54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
54D30 Compactness
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References:

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