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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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