A special point from lozenge and strongly omega-bounded spaces

作者：Dow Alan; Levy Ronnie^*

来源：Topology and Its Applications, 2015, 195: 239-245.

DOI：10.1016/j.topol.2015.09.026

• Strongly omega-bounded
• CNP space
• lozenge
• P-point
• Remote point

A Tychonoff space is CNP if it is a P-set in its Stone-Cech compactification. We are interested in the question of whether the property of being a CNP space is finitely productive. A space X is strongly omega-bounded if every sigma-compact subset of X has compact closure in X. In this paper, we show that the existence of two CNP spaces whose product is not CNP is equivalent to the existence of a space which is not strongly omega-bounded but which is the union of two subsets each of which is strongly omega-bounded. We use lozenge to construct a special point in beta (omega x (beta omega\omega)) and use that point to find a non-strongly omega-bounded space which is a union of two strongly omega-bounded subsets.

• 出版日期2015-11