Barely alternating real almost chains and extension operators for compact lines
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909154199732224 |
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| author | Avilés, Antonio Korpalski, Maciej |
| author_facet | Avilés, Antonio Korpalski, Maciej |
| contents | Assume $\text{MA}(κ)$. We show that for every real chain of size $κ$ in the quotient Boolean algebra $P(ω)/fin$ we can find an almost chain of representatives such that every $n\inω$ oscillates at most three times along the almost chain. This is used to show that for every countable discrete extension of a separable compact line $K$ of weight $κ$ there exists an extension operator $E:C(K)\longrightarrow C(L)$ of norm at most three. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19327 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Barely alternating real almost chains and extension operators for compact lines Avilés, Antonio Korpalski, Maciej Logic Functional Analysis Assume $\text{MA}(κ)$. We show that for every real chain of size $κ$ in the quotient Boolean algebra $P(ω)/fin$ we can find an almost chain of representatives such that every $n\inω$ oscillates at most three times along the almost chain. This is used to show that for every countable discrete extension of a separable compact line $K$ of weight $κ$ there exists an extension operator $E:C(K)\longrightarrow C(L)$ of norm at most three. |
| title | Barely alternating real almost chains and extension operators for compact lines |
| topic | Logic Functional Analysis |
| url | https://arxiv.org/abs/2403.19327 |