t-topology on the n-dimensional Minkowski space
- Department of Mathematics, Dayalbagh Educational Institute (Deemed University), Dayalbagh, Agra, 282005 India (India)
In this paper, a topological study of the n-dimensional Minkowski space, n>1, with t-topology, denoted by M{sup t}, has been carried out. This topology, unlike the usual Euclidean one, is more physically appealing being defined by means of the Lorentzian metric. It shares many topological properties with similar candidate topologies and it has the advantage of being first countable. Compact sets of M{sup t} and continuous maps into M{sup t} are studied using the notion of Zeno sequences besides characterizing those sets that have the same subspace topologies induced from the Euclidean and t-topologies on n-dimensional Minkowski space. A necessary and sufficient condition for a compact set in the Euclidean n-space to be compact in M{sup t} is obtained, thereby proving that the n-cube, n>1, as a subspace of M{sup t}, is not compact, while a segment on a timelike line is compact in M{sup t}. This study leads to the nonsimply connectedness of M{sup t}, for n=2. Further, Minkowski space with s-topology has also been dealt with.
- OSTI ID:
- 21294099
- Journal Information:
- Journal of Mathematical Physics, Vol. 50, Issue 5; Other Information: DOI: 10.1063/1.3129188; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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