Perfectly normal nonrealcompact spaces under Martin's Maximum

• Published in: Mathematical logic quarterly Vol. 70; no. 4; pp. 388 - 397
• Main Author: Ishiu, Tetsuya
• Format: Journal Article
• Language: English
• Published: Berlin Wiley Subscription Services, Inc 01.11.2024

We analyze the behavior of a perfectly normal nonrealcompact space (ω1,τ)$(\omega _1, \tau)$ on ω1$\omega _1$ such that for every γ<ω1$\gamma <\omega _1$, γ$\gamma$ is τ$\tau$‐open and γ+ω$\gamma +\omega$ is τ$\tau$‐closed under Martin's Maximum. We show that there exists a club subset D$...