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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.
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Every and hyperkähler
( Every Calabi – Yau manifold in 4 ( real ) dimensions is a hyperkähler manifold, because SU ( 2 ) is isomorphic to Sp ( 1 ).
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 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.
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 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 Hermitian manifold is a complex manifold which comes naturally equipped with a Hermitian form and an integrable, almost complex structure.
* 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 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 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 M
* In any ring R, a maximal ideal is an ideal M that is maximal in the set of all proper ideals of R, i. e. M is contained in exactly 2 ideals of R, namely M itself and the entire ring R. Every maximal ideal is in fact prime.
Every smooth ( or differentiable ) map φ: M → N between smooth ( or differentiable ) manifolds induces natural linear maps between the corresponding tangent spaces:
Every measurable cardinal κ is a 0-huge cardinal because < sup > κ </ sup > M ⊂ M, that is, every function from κ to M is in M. Consequently, V < sub > κ + 1 </ sub >⊂ M.
: Every countable theory which is satisfiable in a model M, is satisfiable in a countable substructure of M.
* Siegal, M., Cornell Feline Health Center ( Editors ) ( 1989 ) The Cornell Book of Cats: A Comprehensive Medical Reference for Every Cat and Kitten.
Every year about 5000 applications are received, out of which about 300 students ( around 150 in each year ) are enrolled in the 2 year full time M. Tech.
Every finite-length module M has a composition series, and the length of every such composition series is equal to the length of M.
* Every direct summand of M is pure in M. Consequently, every subspace of a vector space over a field is pure.
Every and has
Every woman has had the experience of saying no when she meant yes, and saying yes when she meant no.
Every detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he is playing with Viennese musicians ), and the gossamer shading throughout.
Every family of Riviera Presbyterian Church has been asked to read the Bible and pray together daily during National Christian Family Week and to undertake one project in which all members of the family participate.
Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.
Every such subset has a smallest element, so to specify our choice function we can simply say that it maps each set to the least element of that set.
** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.
The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.
** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.
* Every continuous functor on a small-complete category which satisfies the appropriate solution set condition has a left-adjoint ( the Freyd adjoint functor theorem ).
Every unit of length has a corresponding unit of area, namely the area of a square with the given side length.
Every field has an algebraic extension which is algebraically closed ( called its algebraic closure ), but proving this in general requires some form of the axiom of choice.
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.