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A note on nowhere dense sets in \(\omega^*\). (English) Zbl 0696.54019
The author shows that the famous Hechler’s conjecture is equivalent to a statement concerning the natural order of the family of all nowhere dense subsets of \(\beta\) \(\omega\) \(\setminus \omega:\) Every nowhere dense set in \(\beta\) \(\omega\) \(\setminus \omega\) is a \(2^{\omega}\)-set if and only if every nowhere dense set in \(\beta\) \(\omega\) \(\setminus \omega\) is a nowhere dense subset of another nowhere dense set.

MSC:
54D40 Remainders in general topology
54G05 Extremally disconnected spaces, \(F\)-spaces, etc.
03E05 Other combinatorial set theory
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