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Considering only inertial frames of reference and constant velocities, does the fact that any velocity, with the exception for the speed of light in a vacuum, can be transformed, via an accurate transformation, in any other velocity have something to do with the isotropic property of space and the homogeneity of spacetime?

In particular, in order to maintain this property of velocity, is it necessary that both space and spacetime are respectively isotropic and homogeneous, or is it sufficient that just one of these properties is verified, or maybe none are? Why?

Thank you for you time!

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