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Maximal nowhere dense P-sets in basically disconnected spaces and F-spaces. (English) Zbl 1053.54041
The authors investigate maximal nowhere dense sets in various types of compact spaces (a nowhere dense closed set $$\mathfrak M$$ is maximal if there is no n.d. closed set $$\mathfrak M'$$ containing $$\mathfrak M$$ as a nowhere dense subset). As proved by P. Simon, the statement that there are no maximal n.d. sets in $$\omega ^*$$ is equivalent to the Hechler conjecture.
The authors prove the existence of maximal n.d. sets which are moreover $$P$$-sets for Stone spaces of $$\omega _2$$-complete Boolean algebras. They have more results and characterization in this direction. The authors notice that there are many nowhere dense $$P$$-sets in a basically disconnected non-c.c.c. compact space but under [CH], there is no maximal n.d. $$P$$-set in $$\omega ^*$$.
Reviewer: Jan Pelant (Praha)
##### MSC:
 54G05 Extremally disconnected spaces, $$F$$-spaces, etc. 54D30 Compactness
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