Betweenness relation and isometric imbeddings of metric spaces
We give an elementary proof of the classical Menger result according to which any metric space X that consists of more than four points is isometrically imbedded into \( \mathbb{R} \) if every three-point subspace of X is isometrically imbedded into \( \mathbb{R} \). A series of corollaries of this...
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| Дата: | 2009 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2009
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/3103 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | We give an elementary proof of the classical Menger result according to which any metric space X that consists of more than four points is isometrically imbedded into \( \mathbb{R} \) if every three-point subspace of X is isometrically imbedded into \( \mathbb{R} \). A series of corollaries of this theorem is obtained. We establish new criteria for finite metric spaces to be isometrically imbedded into \( \mathbb{R} \). |
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