Abstract:For a compact monotonically normal space X we prove: (1) $X$ has a dense set of points with a well-ordered neighborhood base (and so $X$ is co-absolute with a compact orderable space); (2) each point of $X$ has a well-ordered neighborhood $\pi $-base (answering a question of Arhangel'skii); (3) $X$ is hereditarily paracompact iff $X$ has countable tightness. In the process we introduce weak-tightness, a notion key to the results above and yielding some cardinal function results on monotonically normal spaces.
Keywords: monotonically normal, compactness, linear ordered spaces
AMS Subject Classification: 54D15, 54D30, 54F05