When studying the motion of particles in space, what are the mathematical considerations that have to made of spacetime? Could I say there exists a bijection between spacetime and ##\mathbb{R}^4##? Is the topology under consideration the usual product topology of ##\mathbb{R}^4##? Are there any other consideration if all I am concerned with is the kinematics of particles in space?(adsbygoogle = window.adsbygoogle || []).push({});

Also, what differs between the mathematical considerations of spacetime for non-relativistic classical mechanics and relativistic mechanics? Is the set not bijective to ##\mathbb{R}^4## anymore? Or is it only the topology defined on ##\mathbb{R}^4## that is different?

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# Mathematical considerations of spacetime in classical mechanics

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