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- W2085317083 abstract "In the space Gn of n-dimensional Lie algebras a new non-Hausdorff topology τ is defined. Here (Gn, τ) is a compact connected T0 space. The closed one-point sets in the noncommutative part of Gn are called atoms. For each n≥3 there exist two atoms. Geroch’s limit defines a topology σ in the space Nn of local homogeneous Riemannian manifolds of dimension n. A natural relation of the Nn to the spaces Gn is given by the Lie algebra corresponding to the isometry group of the elements of Nn. It has nice σ–τ-continuity properties, e.g., the atoms are exactly those elements of Gn that correspond to closed nonempty subsets in the nonflat part of Nn. Applying to cosmology, especially for cosmological models with intrinsically homogeneous slices t=const, a complete answer to the question of how the isometry group of the spacelike hypersurfaces may depend on time is given: The slices are σ-continuous and their isometry groups are τ-continuous functions of time t. Applications of σ and τ to other problems are sketched." @default.
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- W2085317083 date "1987-08-01" @default.
- W2085317083 modified "2023-09-27" @default.
- W2085317083 title "On Geroch’s limit of space-times and its relation to a new topology in the space of Lie groups" @default.
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- W2085317083 doi "https://doi.org/10.1063/1.527457" @default.
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