Variations on tightness in function spaces

✍ Scribed by Masami Sakai

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 99 KB
• Volume: 101
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(98)00127-8

✦ Synopsis

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 proved that the tightness of C p (X) is countable if and only if every finite power of X is Lindelöf. In this paper, we give topological properties of X which characterize T -tightness and settightness of C p (X). A characterization of set-tightness of C p (X) answers a question posed by Bella.