T -topology on the n-dimensional Minkowski space

Abstract

In this paper, a topological study of the n-dimensional Minkowski space, n>1, with t-topology, denoted by Mt, 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 Mt and continuous maps into Mt 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 Mt is obtained, thereby proving that the n-cube, n>1, as a subspace of Mt, is not compact, while a segment on a timelike line is compact in Mt. This study leads to the nonsimply connectedness of Mt, for n=2. Further, Minkowski space with s-topology has also been dealt with.