Geometric properties of metric spaces
We study some problems of geometrization of arbitrary metric spaces. In particular, we studied the concept of straight and flat placement of points in this space. In a certain way, we continue the investigations of Kagan devoted to the detailed analysis of the notion of straightforwardness based on...
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| Datum: | 2019 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2019
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/1446 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | We study some problems of geometrization of arbitrary metric spaces. In particular, we studied the concept of straight and
flat placement of points in this space. In a certain way, we continue the investigations of Kagan devoted to the detailed
analysis of the notion of straightforwardness based on four groups of postulates. The results of our work are based on the
notion of angular characteristics of three points of the space proposed by Alexandrov. We establish the conditions under
which the set of points of an arbitrary metric space satisfies all five postulates of the first group of Kagan’s placement
postulates. The relationship between rectilinear and flat placements of points of the metric space is investigated. Examples
of placements of this kind based on linear functions in some classical spaces are presented. The results of the paper
are obtained without using the property of completeness of the space and can be used for the discrete computation and
structuring of specific metric spaces. |
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