Carregant...
Fitxers
Tipus de document
ArticleVersió
Versió acceptadaData de publicació
Tots els drets reservats
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/194104
Constructions of Lindelöf scattered P-spaces
Títol de la revista
Director/Tutor
ISSN de la revista
Títol del volum
Recurs relacionat
Resum
We construct locally Lindelöf scattered P-spaces (LLSP spaces, for short) with prescribed widths and heights under different set-theoretic assumptions. We prove that there is an LLSP space of width $\omega_1$ and height $\omega_2$ and that it is relatively consistent with ZFC that there is an LLSP space of width $\omega_1$ and height $\omega_3$. Also, we prove a stepping up theorem which, for every cardinal $\lambda \geq \omega_2$, permits us to construct from an LLSP space of width $\omega_1$ and height $\lambda$ satisfying certain additional properties an LLSP space of width $\omega_1$ and height $\alpha$ for every ordinal $\alpha<\lambda^{+}$. As consequences of the above results, we obtain the following theorems: (1) For every ordinal $\alpha<\omega_3$ there is an LLSP space of width $\omega_1$ and height $\alpha$. (2) It is relatively consistent with ZFC that there is an LLSP space of width $\omega_1$ and height $\alpha$ for every ordinal $\alpha<\omega_4$.
Matèries (anglès)
Citació
Citació
MARTÍNEZ ALONSO, Juan carlos, SOUKUP, Lajos. Constructions of Lindelöf scattered P-spaces. _Fundamenta Mathematicae_. 2022. Vol. 259, núm. 3, pàgs. 271-286. [consulta: 23 de gener de 2026]. ISSN: 0016-2736. [Disponible a: https://hdl.handle.net/2445/194104]