Pathology of submeasures and $F_σ$ ideals
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916217819758592 |
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| author | Martínez, Jorge Meza-Alcántara, David Uzcátegui, Carlos |
| author_facet | Martínez, Jorge Meza-Alcántara, David Uzcátegui, Carlos |
| contents | We address some phenomena about the interaction between lower semicontinuous submeasures on $\mathbb{N}$ and $F_σ$ ideals. We analyze the pathology degree of a submeasure and present a method to construct pathological $F_σ$ ideals. We give a partial answers to the question of whether every nonpathological tall $F_σ$ ideal is Katětov above the random ideal or at least has a Borel selector. Finally, we show a representation of nonpathological $F_σ$ ideals using sequences in Banach spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_01544 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Pathology of submeasures and $F_σ$ ideals Martínez, Jorge Meza-Alcántara, David Uzcátegui, Carlos Functional Analysis General Topology Logic We address some phenomena about the interaction between lower semicontinuous submeasures on $\mathbb{N}$ and $F_σ$ ideals. We analyze the pathology degree of a submeasure and present a method to construct pathological $F_σ$ ideals. We give a partial answers to the question of whether every nonpathological tall $F_σ$ ideal is Katětov above the random ideal or at least has a Borel selector. Finally, we show a representation of nonpathological $F_σ$ ideals using sequences in Banach spaces. |
| title | Pathology of submeasures and $F_σ$ ideals |
| topic | Functional Analysis General Topology Logic |
| url | https://arxiv.org/abs/2211.01544 |