Weak p-points can be but need not be o-points (Q803998)

Properties of points of Stone-Čech growth \(N^*=\beta N\setminus N\) of the countable discretum N are considered. The notation of \textit{A. A. Gryzlov} [``On the hereditary normality of spaces \(\beta\omega\setminus \omega ''\) in: Topology and set theory, Izhėvsk, (Russ.), No.3, 61-64 (1982); ``On the theory of the space \(\beta N\)'' in General Topology: Mapping of Topological spaces, Moskva 1986 (Russ.), 20-34] will be employed. It is known that p-points are o-points in the space \(N^*\) [\textit{M. E. Rudin}, Types of ultrafilters, Topology Seminar, vol. 145, Wisconsin 1965, see also Ann. Math. Stud. 60, 147-151 (1966; Zbl 0158.201)]. However, o-points exist ``naively'' [the second of the cited papers of Gryzlov], while p-points exist only under additional set- theoretic constraints. A ``naive'' analog of p-points is provided by weak p-points, in particular Gryzlov matrix points. They possess stronger properties than in the case of another type of weak p-points, namely the c-ok-points introduced by \textit{K. Kunen} [Topology, Vol. 2, 4th Colloq. Budapest 1978, Colloq. Soc. János Bolyai 23, 741-749 (1980; Zbl 0435.54021)]. Matrix points are c-ok-points; the converse is not true. In addition, they are strict R-points, and, hence, R-points and non- normality points. These implications are unknown for c-ok-points.