例句與造句

1. Not all vector spaces with complete translation-invariant metrics are Fr閏het spaces.
2. Fr閏het spaces are locally convex spaces that are complete with respect to a translation invariant metric.
3. The space for is an F-space : it admits a complete translation-invariant metric with respect to which the vector space operations are continuous.
4. A "'compact Riemannian nilmanifold "'is a compact Riemannian manifold which is locally isometric to a nilpotent Lie group with left-invariant metric.
5. More precisely, seven of the 8 geometries can be realized as a left-invariant metric on the simply connected group ( sometimes in more than one way ).
6. It's difficult to find invariant metric in a sentence. 用invariant metric造句挺難的
7. Every locally compact group which is second-countable is metrizable as a topological group ( i . e . can be given a left-invariant metric compatible with the topology ) and complete.
8. The requirement that the transitive nilpotent group acts by isometries leads to the following rigid characterization : every homogeneous nilmanifold is isometric to a nilpotent Lie group with left-invariant metric ( see Wilson ).
9. This distance provides a right-invariant metric of diffeomorphometry, invariant to reparameterization of space since for all \ varphi \ in \ operatorname { Diff } _ V \, \, \,,
10. This geometry can be modeled as a left invariant metric on the Bianchi group of type II . Finite volume manifolds with this geometry are compact and orientable and have the structure of a Seifert fiber space.
11. If the locally compact abelian group " G " is separable and metrizable ( its topology may be defined by a translation-invariant metric ) then harmonious sets admit another, related, description.
12. Instead, with the topology of compact convergence, C can be given the structure of a Fr閏het space : a locally convex topological vector space whose topology can be induced by a complete translation-invariant metric.
13. Indeed, a topological vector space is called complete iff its uniformity ( induced by its topology and addition operation ) is complete; the uniformity induced by a translation-invariant metric that induces the topology coincides with the original uniformity.
14. Born and H . S . Green similarly introduced the notion an invariant ( quantum ) metric operator x _ k x ^ k + p _ k p ^ k as extension of the Minkowski metric of special relativity to an invariant metric on phase space coordinates.
15. *The space of measurable functions on the unit interval ( where we identify two functions that are equal almost everywhere ) has a vector-space topology defined by the translation-invariant metric : ( which induces the convergence in measure of measurable functions; for random variables, convergence in measure is convergence in probability)
16. More generally, whenever one has a compact group with Haar measure ?, and an arbitrary inner product " h ( X, Y ) " defined at the tangent space of some point in " G ", one can define an invariant metric simply by averaging over the entire group, i . e . by defining
更多例句：  下一頁