Normal spaces whose Stone-Čech remainders have countable tightness
Abstract: We prove, assuming PFA, that each normal space whose Stone-Čch remainder has countable tightness is ACRIN. A normal space is called ACRIN if each of its regular images is normal. Fleissner and Levy proved that if is normal and every countably compact subset of the Stone-Čech remainder is closed in , then is ACRIN. They asked if each normal space whose Stone-Čech remainder has countable tightness is ACRIN. Theorem gives the positive answer assuming the Proper Forcing Axiom.
- [Ba] Zoltán T. Balogh, On compact Hausdorff spaces of countable tightness, Proc. Amer. Math. Soc. 105 (1989), no. 3, 755–764. MR 930252, https://doi.org/10.1090/S0002-9939-1989-0930252-6
- [FL] William Fleissner and Ronnie Levy, Stone-Čech remainders which make continuous images normal, Proc. Amer. Math. Soc. 106 (1989), no. 3, 839–842. MR 963571, https://doi.org/10.1090/S0002-9939-1989-0963571-8
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54D40
Retrieve articles in all journals with MSC: 54D40