On the completions of the spaces of metrics on an open manifold. II (Q1377206)
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scientific article; zbMATH DE number 1112242
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the completions of the spaces of metrics on an open manifold. II |
scientific article; zbMATH DE number 1112242 |
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On the completions of the spaces of metrics on an open manifold. II (English)
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14 September 1998
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A complete metric is constructed on the set \({\mathcal S}(X)\) of semi-metrics on a set \(X\). It is shown that a number of subsets of \({\mathcal S} (X)\) are closed, hence also complete, with respect to the metric. The ideas are then applied to the space of \(m\) times continuously differentiable Riemannian metrics on a smooth metrisable manifold. The main result links a metric on a component of this space with a uniform structure. [For part I see \textit{G. Salomonsen}, ibid. 29, No. 3-4, 355-360 (1996; Zbl 0864.58005)].
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space of metrics
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complete metrics on the set of semi-metrics
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0.88855875
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