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Order-like structure of monotonically normal spaces

Scott W. Williams;  Hao Xuan Zhou — 1998

Commentationes Mathematicae Universitatis Carolinae

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 π -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...

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