locally euclidean sentence in Hindi
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- Every manifold has a natural topology since it is locally Euclidean.
- The property of being locally Euclidean is preserved by local homeomorphisms.
- This much is a fragment of a typical locally Euclidean topological group.
- In particular, being locally Euclidean is a topological property.
- It is true, however, that every locally Euclidean space is T 1.
- A "'topological manifold "'is a locally Euclidean Hausdorff space.
- An example of a non-Hausdorff locally Euclidean space is the line with two origins.
- The definition I follow is the " locally Euclidean " one so I allow the long line to be a manifold.
- In the previous section, a surface is defined as a topological space with certain properties, namely Hausdorff and locally Euclidean.
- There are also topological manifolds, i . e ., locally Euclidean spaces, which possess no differentiable structures at all.
- However, this is just the most likely reason as to why people don't study non-locally Euclidean topological spaces.
- The Hausdorff property is not a local one; so even though Euclidean space is Hausdorff, a locally Euclidean space need not be.
- The theorem has a number of equivalent statements, one of which is that the topology induced by the Carnot Carath�odory metric is equivalent to the intrinsic ( locally Euclidean ) topology of the manifold.
- Quasi-projective varieties are " locally affine " in the sense that a manifold is locally Euclidean & mdash; every point of a quasiprojective variety has a neighborhood given by an affine variety.
- But anyhow, differenciation involves the notion of'direction'and arbitrary topological space don't have this notion unless you have a local vector space structure defined on them ( for instance locally Euclidean ).
- The polyhedron can be thought of as being folded from a sheet of paper ( a homeomorphic ( topologically equivalent ) to a sphere, and locally Euclidean except for a finite number of cone points whose angular defect sums to 4.
- Where the latter equals to zero, the metric structure is locally Euclidean ( it means that at least some open set in the coordinate space is isometric to a piece of Euclidean space ), no matter whether coordinates are affine or curvilinear.
- The " unrestricted " version of Hilbert's fifth problem, closer to Hilbert's original formulation, considers both a locally Euclidean group " G " and another manifold " M " on which " G " has a continuous action.
- A topological manifold is a locally Euclidean Hausdorff space . ( In Wikipedia, a manifold need not be paracompact or second-countable . ) A " C k " manifold is a differentiable manifold whose chart overlap functions are " k " times continuously differentiable.
- A space " M " is locally Euclidean if and only if it can be atlas "'on " M " . ( The terminology comes from an analogy with cartography whereby a spherical globe can be described by an atlas of flat maps or charts ).
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