For a Tychonoff space X we denote by C p (X) the space of all real-valued continuous functions on X with the topology of pointwise convergence. It is known that some topological properties of C p (X) can be well characterized by topological properties of X. For example, Arhangel'skii and Pytkeev pro
Attainment of Tightness in Boolean Spaces
✍ Scribed by Juan Carlos Martínez
- Publisher
- John Wiley and Sons
- Year
- 2002
- Tongue
- English
- Weight
- 101 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
✦ Synopsis
We consider some questions of Donald Monk related to attainment of the tightness function in Boolean spaces. Then we prove in ZFC that attainment of tightness in the sense of the definition does not imply attainment of tightness in the free sequence sense. Our results give rise to full answers to Problems 41, 42].
📜 SIMILAR VOLUMES
Theorem A. There is a superatomic Boolean algebra B with size and n-character equal to WI and countable depth. Theorem B. If B is a superatomic Boolean algebra with r-character greater than WI, then the 7r-character and depth of B are the same. Theorem C. rf rc. --f (K):~, then every superatomic Boo