Geodesic
Order-like structure of monotonically normal spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 1, pp. 207-217 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 54D15, 54D30, 54F05
Keywords: monotonically normal; compactness; linear ordered spaces 
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     title = {Order-like structure of monotonically normal spaces},
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     pages = {207--217},
     year = {1998},
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Williams, Scott W.; Zhou, Haoxuan. Order-like structure of monotonically normal spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 1, pp. 207-217. http://geodesic.mathdoc.fr/item/CMUC_1998_39_1_a20/