Compactifications and remainders of monotonically normal spaces

Monotonically normal spaces have many strong properties, but poor preservation properties. For example, there are locally compact, monotonically normal spaces whose one-point compactifications are not monotonically normal, and hence have no monotonically normal compactifications. We give two classes of such spaces, and give a pair of necessary conditions for spaces of pointwise countable type to have, respectively, compactifications or remainders that are monotonically normal. We show that a monotonically normal, locally compact space has a monotonically normal compactification if it is either locally connected or countably compact, and show that this latter condition cannot be weakened to “σ-countably compact.”