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.

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. 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, nonsecond countable, noncompact, and non-Lindelöf.

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In this paper, we obtain the projective cover of the orbit space X/G in terms of the orbit space of the projective space of X, when X is a Tychonoff G-space and G is a finite discrete group. An example shows that flniteness of G is needed.