Applications of independent linked families. (English) Zbl 0615.54004

Simon, P.

Topology theory and applications, 5th Colloq., Eger/Hung. 1983, Colloq. Math. Soc. János Bolyai 41, 561-580 (1985).

[For the entire collection see Zbl 0588.00022.]
Weak p-points and \({\mathbb{C}}\)-OK points are used to prove the following results: (1) No infinite compact F-space is subhomogeneous. This generalizes Frolik’s theorem that no infinite compact F-space is homogeneous. (2) An extremally disconnected space of weight \(\leq {\mathbb{C}}\) is homeomorphic to a \({\mathbb{C}}\)-OK subset of \(\omega^*\). This generalizes the fact that such spaces embed in \(\omega^*\). (3) There are \(2^{{\mathbb{C}}}\) pairwise RK-incomparable RF-minimal points in \(\omega^*\), where RK is the Rudin-Keisler order, and RF the Rudin- Frolik order. This generalizes the theorem of Shelah that there are \(2^{{\mathbb{C}}}\) pairwise RK-incomparable points in \(\omega^*\).

Reviewer: J.Roitman

MSC:

54A25	Cardinality properties (cardinal functions and inequalities, discrete subsets)
54D40	Remainders in general topology

Keywords:

Weak p-points; \({bbfC}\)-OK points; compact F-space; extremally disconnected space; RF-minimal points; Rudin-Keisler order; Rudin-Frolik order; RK-incomparable points

Citations:

Zbl 0588.00022