A study of non-Euclidean \(s\)-topology. (English) Zbl 1250.53020
Summary: The present paper focuses on the characterization of compact sets of Minkowski space with a non-Euclidean \(s\)-topology which is defined in terms of the Lorentz metric. As an application of this study, it is proved that the 2-dimensional Minkowski space with \(s\)-topology is not simply connected. Also, it is obtained that the \(n\)-dimensional Minkowski space with \(s\)-topology is separable, first countable, path-connected, nonregular, nonmetrizable, not second countable, noncompact, and non-Lindelöf.
MSC:
| 53B30 | Local differential geometry of Lorentz metrics, indefinite metrics |
| 53A35 | Non-Euclidean differential geometry |
| 51B20 | Minkowski geometries in nonlinear incidence geometry |
References:
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