# Continuity in Minkowski space

How "continuity" of a map Τ:M→M, where M is a Minkowski space, can be defined? Obviously I cannot use the "metric" induced by the minkowskian product:
x$\cdot$y = -x$^{0}$y$^{0}$+x$^{i}$y$^{i}$
for the definition of coninuity; it is a misinformer about the proximity of points. Should I use the Euclidean metric instead?

Thank's...

WannabeNewton
Minkowski space-time is just ##\mathbb{R}^{4}## with the canonical Euclidean topology. Continuity of endomorphisms of Minkowski space-time is with respect to this topology.

• 1 person
I took the wikipedia's definition of Minkowski space: a 4-D real vector space with a symmetric, bilinear, non-degenerate quadratic form with signature (1,3). From this point of view, can a consistent metric induced by that quadratic form? If not, then according to your comment, I will have to make use and of the Eucliden norm on that vector space, in order to define continuity.

Right?

WannabeNewton
• The beautiful $$\displaystyle book "The Geometry of Minkowski Spacetime: An Introduction to the Mathematics of the Special Theory of Relativity" by Naber has an appendix that discusses topology for Minkowski spacetime.$$