On nowhere dense ccc -sets

Authors:
Alan Dow and Jan van Mill

Journal:
Proc. Amer. Math. Soc. **80** (1980), 697-700

MSC:
Primary 54D20

MathSciNet review:
587958

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Abstract: We prove that no compact Hausdorff space can be covered by nowhere dense ccc *P*-sets. As an application it follows that if *X* is a compact Hausdorff space with a nonisolated *P*-point then is not homogeneous for any compact ccc space *K*.

**[B]**M. Bell,*A compactification**of N with**ccc nonseparable*(to appear).**[FM]**R. Frankiewicz and C. F. Mills,*More on nowhere dense closed P-sets*(to appear).**[K]**K. Kunen,*Weak P-points in*, Proc. Bolyai János Soc. Colloq. Topology, (Budapest, 1978) (to appear).**[KvMM]**Kenneth Kunen, Jan van Mill, and Charles F. Mills,*On nowhere dense closed 𝑃-sets*, Proc. Amer. Math. Soc.**78**(1980), no. 1, 119–123. MR**548097**, 10.1090/S0002-9939-1980-0548097-X**[vM]**Jan van Mill,*Weak 𝑃-points in compact 𝐹-spaces*, The Proceedings of the 1979 Topology Conference (Ohio Univ., Athens, Ohio, 1979), 1979, pp. 609–628 (1980). MR**598298****[vM]**Jan van Mill,*A remark on the Rudin-Keisler order of ultrafilters*, Houston J. Math.**9**(1983), no. 1, 125–129. MR**699055**

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DOI:
https://doi.org/10.1090/S0002-9939-1980-0587958-2

Keywords:
*P*-set,
independent matrix,
ccc,
homogeneous

Article copyright:
© Copyright 1980
American Mathematical Society