C-points vs P-points and P-points

[摘要] In a Tychonoff space X, the point p\in X is called a C^*-point if every real-valued continuous function on C\smallsetminus \{p\} can be extended continuously to p. Every point in an extremally disconnected space is a C^*-point. A classic example is the space {\bf W}^*=\omega_1+1 consisting of the countable ordinals together with \omega_1. The point \omega_1 is known to be a C^*-point as well as a P-point. We supply a characterization of C^*-points in totally ordered spaces. The remainder of our time is aimed at studying when a point in a product space is a C^*-point. This process leads to many interesting new discoveries.

[学科分类] 物理化学和理论化学

[关键词] ring of continuous functions;C^*-embedded;P-point