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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2412.05336 |
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| _version_ | 1866915533032521728 |
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| author | Cuong, Nguyen Duy Kruger, Alexander Y. |
| author_facet | Cuong, Nguyen Duy Kruger, Alexander Y. |
| contents | We show that the existing generalized separation statements including the conventional extremal principle and its extensions differ {in the ways norms on product spaces are defined}. We prove a general separation statement with arbitrary product norms covering the existing results of this kind. The proof is divided into a series of claims and exposes the key steps and arguments used when proving generalized separation statements. As an application, we prove dual necessary (sufficient) conditions for an abstract product norm extension of the approximate stationarity (transversality) property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05336 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Separation of Collections of Sets Cuong, Nguyen Duy Kruger, Alexander Y. Functional Analysis Optimization and Control We show that the existing generalized separation statements including the conventional extremal principle and its extensions differ {in the ways norms on product spaces are defined}. We prove a general separation statement with arbitrary product norms covering the existing results of this kind. The proof is divided into a series of claims and exposes the key steps and arguments used when proving generalized separation statements. As an application, we prove dual necessary (sufficient) conditions for an abstract product norm extension of the approximate stationarity (transversality) property. |
| title | Generalized Separation of Collections of Sets |
| topic | Functional Analysis Optimization and Control |
| url | https://arxiv.org/abs/2412.05336 |