Open sets in Minkowski spacetime

Question

I don't know how to imagine open sets in Minkowski spacetime. I have seen that there are many diffrent ways of constructing them — that's OK. But for example. which construction do people mean in the case of the Reeh-Schlieder theorem?

In such an example, do I have to imagine balls in 4-dimensional Euclidean spacetime (simply treating time as additional axis) and forget about lightcones and stuff?

Answer 1

Topologically, Minkowski spacetime is $\mathbb{R}^4$, and most (all?) spacetimes you'll ever see are products of common spaces like Euclidean spaces, spheres, tori, etc. The metric is irrelevant; strictly speaking, the topology comes before.

So yes, one possible basis is the set of open balls of Euclidean space.