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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.19555 |
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| _version_ | 1866913722755186688 |
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| author | Iwamoto, Yutaka |
| author_facet | Iwamoto, Yutaka |
| contents | We show that lattice isomorphisms between lattices of slowly oscillating functions on chain-connected proper metric spaces induce coarsely equivalent homeomorphisms. This result leads to a Banach-Stone-like theorem for these lattices. Furthermore, we provide a representation theorem that characterizes linear lattice isomorphisms among these lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19555 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lattices of slowly oscillating functions Iwamoto, Yutaka General Topology 46E05, 54C35 We show that lattice isomorphisms between lattices of slowly oscillating functions on chain-connected proper metric spaces induce coarsely equivalent homeomorphisms. This result leads to a Banach-Stone-like theorem for these lattices. Furthermore, we provide a representation theorem that characterizes linear lattice isomorphisms among these lattices. |
| title | Lattices of slowly oscillating functions |
| topic | General Topology 46E05, 54C35 |
| url | https://arxiv.org/abs/2405.19555 |