Strongly τ-pseudocompact spaces

✍ Scribed by A.V. Arhangel'skii

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 933 KB
• Volume: 89
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(97)00220-4

✦ Synopsis

A new notion of a strongly T-pseudocompact space is introduced, and its relation to the notion of initially T-compact space is studied. A theorem of J.F. Kennison (Kennison, 1962) is generalized to this case, which leads to new interesting questions. In particular, it is proved that every strongly 2"pseudocompact space of countable tightness is compact, and that every strongly 2"-pseudocompact space is initially T+-compact. It is also established that every wi-pseudocompact topological group of countable tightness is metrizable and, therefore, compact. Several open problems are formulated.