[permalink] [id link]
Every smooth manifold defined in this way has a natural diffeology, for which the plots correspond to the smooth maps from open subsets of R < sup > n </ sup > to the manifold.
from
Wikipedia
Some Related Sentences
Every and smooth
Every smooth ( or differentiable ) map φ: M → N between smooth ( or differentiable ) manifolds induces natural linear maps between the corresponding tangent spaces:
Every smooth submanifold of R < sup > n </ sup > has an induced Riemannian metric g: the inner product on each tangent space is the restriction of the inner product on R < sup > n </ sup >.
Every smooth function G over the symplectic manifold generates a one-parameter family of symplectomorphisms and if
* Every bundle of Lie algebras over a smooth manifold defines a Lie algebroid where the Lie bracket is defined pointwise and the anchor map is equal to zero.
Every smooth surface S has a unique affine plane tangent to it at each point.
Every Sámi settlement had its seita, which had no regular shape, and might consist of smooth or odd-looking stones picked out of a stream, of a small pile of stones, of a tree-stump, or of a simple post.
Every compact smooth manifold of dimension 2n, which has only handles of index ≤ n, has a Stein structure provided n > 2, and when n = 2 the same holds provided the 2-handles are attached with certain framings ( framing less than the Thurston-Bennequin framing ).
Every closed smooth 4-manifold is a union of two Stein 4-manifolds glued along their common boundary.
Every sufficiently smooth DAE is almost everywhere reducible to this semi-explicit index-1 form.
* Every smooth Hilbert manifold can be smoothly embedded onto an open subset of the model Hilbert space.
* Every continuous plurisubharmonic function can be obtained as a limit of monotonically decreasing sequence of smooth plurisubharmonic functions.
Every camp has one or two directors ; the job of the director is to make the camp run smooth and mostly safe without losing the free-spirited and cosy experience of the camp.
Every and manifold
* Every Lie group is parallelizable, and hence an orientable manifold ( there is a bundle isomorphism between its tangent bundle and the product of itself with the tangent space at the identity )
Every Riemann surface is a two-dimensional real analytic manifold ( i. e., a surface ), but it contains more structure ( specifically a complex structure ) which is needed for the unambiguous definition of holomorphic functions.
Every Kähler manifold is also a symplectic manifold.
* Every Lie algebra is a Lie algebroid over the one point manifold.
Every Hermitian manifold is a complex manifold which comes naturally equipped with a Hermitian form and an integrable, almost complex structure.
Every closed manifold is the boundary of the non-compact manifold.
Every closed manifold is such that, so for every.
Every complex manifold is itself an almost complex manifold.
Every hyperkähler manifold M has a 2-sphere of complex structures ( i. e. integrable almost complex structures ) with respect to which the metric is Kähler.
( Every Calabi – Yau manifold in 4 ( real ) dimensions is a hyperkähler manifold, because SU ( 2 ) is isomorphic to Sp ( 1 ).
Every compact manifold is its own soul.
* The embedding theorem for Stein manifolds states the following: Every Stein manifold of complex dimension can be embedded into by a biholomorphic proper map.
* Every Stein manifold is holomorphically spreadable, i. e. for every point, there are holomorphic functions defined on all of which form a local coordinate system when restricted to some open neighborhood of.
Every complete, connected, simply-connected manifold of constant negative curvature − 1 is isometric to the real hyperbolic space H < sup > n </ sup >.
Every manifold has an underlying topological manifold, obtained simply by forgetting the additional structure.
Every and defined
Every ATM cell has an 8-or 12-bit Virtual Path Identifier ( VPI ) and 16-bit Virtual Channel Identifier ( VCI ) pair defined in its header.
Every normed vector space V sits as a dense subspace inside a Banach space ; this Banach space is essentially uniquely defined by V and is called the completion of V.
Every meromorphic function on D can be expressed as the ratio between two holomorphic functions ( with the denominator not constant 0 ) defined on D: any pole must coincide with a zero of the denominator.
Every computable relation is defined to be and.
Every delta operator ' has a unique sequence of " basic polynomials ", a polynomial sequence defined by three conditions:
Every free abelian group has a rank defined as the cardinality of a basis.
Every locally constant function from the real numbers R to R is constant by the connectedness of R. But the function f from the rationals Q to R, defined by f ( x ) = 0 for x < π, and f ( x ) = 1 for x > π, is locally constant ( here we use the fact that π is irrational and that therefore the two sets
Every Boolean algebra is a Heyting algebra when a → b is defined as usual as ¬ a ∨ b, as is every complete distributive lattice when a → b is taken to be the supremum of the set of all c for which a ∧ c ≤ b. The open sets of a topological space form a complete distributive lattice and hence a Heyting algebra.
* Every Polish space is obtained as a continuous image of Baire space ; in fact every Polish space is the image of a continuous bijection defined on a closed subset of Baire space.
Every definition existing in the CIM repository is initially defined in an MOF file.
Every important sector of the ' big media ' today -- film, records, radio, and cable TV -- was born of a kind of piracy so defined.
Every rotation in three dimensions is defined by its axis — a direction that is left fixed by the rotation — and its angle — the amount of rotation about that axis ( Euler rotation theorem ).
Every special uniformly continuous real-valued function defined on the metric space is uniformly approximable by means of Lipschitz functions.
Every algebraic plane curve has a degree, which can be defined, in case of an algebraically closed field, as number of intersections of the curve with a generic line.
Every closure operator on a poset has many fixed points ; these are the " closed elements " with respect to the closure operator, and they are the main reason the closure operator was defined in the first place.
Every frame the program toggles drawing either the vehicle and road hazards or the road posts that defined the track.
Every isogeny f: A → B is automatically a group homomorphism between the groups of k-valued points of A and B, for any field k over which f is defined.
Every cotree T defines a cograph G having the leaves of T as vertices, and in which the subtree rooted at each node of T corresponds to the induced subgraph in G defined by the set of leaves descending from that node:
Every self-adjoint operator is densely defined, closed and symmetric.
Every product can be defined by its market niche.
* Every compact set is totally bounded, whenever the concept is defined.
Every length of cloth is stamped with the official Orb symbol, trademarked by the Harris Tweed Association in 1909, when Harris Tweed was defined as " hand-spun, hand-woven and dyed by the crofters and cottars in the Outer Hebrides.
0.899 seconds.