Abstract
The present paper focuses on the characterization of compact sets of Minkowski space with a non-Euclidean -topology which is defined in terms of Lorentz metric. As an application of this study, it is proved that the 2-dimensional Minkowski space with -topology is not simply connected. Also, it is obtained that the -dimensional Minkowski space with -topology is separable, first countable, path-connected, nonregular, nonmetrizable, nonsecond countable, noncompact, and non-Lindelöf.
Highlights
Non-Euclidean topologies on 4-dimensional Minkowski space were first introduced by Zeeman 1 in 1967
The present paper focuses on the characterization of compact sets of Minkowski space with a nonEuclidean s-topology which is defined in terms of Lorentz metric
The present paper explores the s-topology on n-dimensional Minkowski space
Summary
Non-Euclidean topologies on 4-dimensional Minkowski space were first introduced by Zeeman 1 in 1967. Studying the homeomorphism group of 4-dimensional Minkowski space with fine topology, Zeeman in his paper 1 mentioned that it is Hausdorff, connected, locally connected space that is not normal, not locally compact and not first countable. His results were interesting both topologically and physically, because its homeomorphism group was the group generated by the Lorentz group, translations and dilatations which was exactly the one physicists would want it to be. ISRN Mathematical Physics the fine topology is separable, Hausdorff, nonnormal, nonlocally compact, non-Lindeloff and nonfirst countable He further obtained that 2-dimensional Minkowski space with fine topology is path connected but not connected and characterized its compact sets.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
