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DC Field | Value | Language |
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dc.contributor.author | Martínez Alonso, Juan Carlos | - |
dc.contributor.author | Soukup, Lajos | - |
dc.date.accessioned | 2023-02-24T08:11:45Z | - |
dc.date.available | 2023-02-24T08:11:45Z | - |
dc.date.issued | 2022-09-20 | - |
dc.identifier.issn | 0016-2736 | - |
dc.identifier.uri | http://hdl.handle.net/2445/194104 | - |
dc.description.abstract | 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 $\alpha<\omega_4$. | - |
dc.format.extent | 16 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | Institute of Mathematics, Polish Academy of Sciences | - |
dc.relation.isformatof | Versió postprint del document publicat a: https://doi.org/10.4064/fm228-7-2022 | - |
dc.relation.ispartof | Fundamenta Mathematicae, 2022, vol. 259, num. 3, p. 271-286 | - |
dc.relation.uri | https://doi.org/10.4064/fm228-7-2022 | - |
dc.rights | (c) Institute of Mathematics, Polish Academy of Sciences, 2022 | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Nombres cardinals | - |
dc.subject.classification | Teoria de conjunts | - |
dc.subject.classification | Topologia | - |
dc.subject.classification | Espais topològics | - |
dc.subject.other | Cardinal numbers | - |
dc.subject.other | Set theory | - |
dc.subject.other | Topology | - |
dc.subject.other | Topological spaces | - |
dc.title | Constructions of Lindelöf scattered P-spaces | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/acceptedVersion | - |
dc.identifier.idgrec | 726103 | - |
dc.date.updated | 2023-02-24T08:11:45Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
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726103.pdf | 175.83 kB | Adobe PDF | View/Open |
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