The -topology on compact spaces
Transfinite cardinal dimension and separability
Paracompactness in box products
Order-like structure of monotonically normal spaces
For a compact monotonically normal space X we prove: (1) has a dense set of points with a well-ordered neighborhood base (and so is co-absolute with a compact orderable space); (2) each point of has a well-ordered neighborhood -base (answering a question of Arhangel’skii); (3) is hereditarily paracompact iff 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...
On the multiple Birkhoff recurrence theorem in dynamics
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