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It is not the case that The requirements of homogeneity and isotropy for physical space, as held by Helmholtz and Lie, are valid only for a matter-empty universe.
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1.
Helmholtz and Lie require homogeneity and isotropy as characteristics of physical space.
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2.
From a general Riemannian standpoint, homogeneity and isotropy hold only in a matter-empty universe.
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