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monotonically normal; compactness; linear ordered spaces
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.
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