## Scott W. Williams, Haoxuan Zhou

*Order-like structure of monotonically normal spaces *

Comment.Math.Univ.Carolinae 39,1 (1998) 207-217. **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

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