t-topology on the n-dimensional Minkowski space

摘要

In this paper, a topological study of the n-dimensional Minkowski space, n> 1,with t-topology, denoted by M~t,has been carried out. This topology, unlike theusual Euclidean one, is more physically appealing being defined by means of theLorentzian metric. It shares many topological properties with similar candidatetopologies and it has the advantage of being first countable. Compact sets of M~tandcontinuous maps into M~tare studied using the notion of Zeno sequences besidescharacterizing those sets that have the same subspace topologies induced from theEuclidean and t-topologies on n-dimensional Minkowski space. A necessary andsufficient condition for a compact set in the Euclidean n-space to be compact in M~tis obtained, thereby proving that the n-cube, n> 1, as a subspace of M~t,is notcompact, while a segment on a timelike line is compact in M~t.This study leads tothe nonsimply connectedness of M~t,forn=2.Further, Minkowski space withs-topology has also been dealt with.