Constructions of Lindelöf scattered P-spaces
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 s...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/194104 |
| Acceso en línea: | https://hdl.handle.net/2445/194104 |
| Access Level: | acceso abierto |
| Palabra clave: | Nombres cardinals Teoria de conjunts Topologia Espais topològics Cardinal numbers Set theory Topology Topological spaces |
| Sumario: | 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 $\alpha<\omega_4$. |
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