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Every smooth ( or differentiable ) map φ: M → N between smooth ( or differentiable ) manifolds induces natural linear maps between the corresponding tangent spaces:

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## Some Related Sentences

Every and smooth

__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__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__

__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__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____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 map

*

__Every__continuous__map__from a compact space to a Hausdorff space is closed and proper**(**i. e.,**the**pre-image of a compact set is compact.__Every__continuous

__map__f

**:**X

**→**Y

**induces**an algebra homomorphism C

**(**f

**)**

**:**C

**(**Y

**)**

**→**C

**(**X

**)**by

**the**rule C

**(**f )(

**φ**

**)**=

**φ**o f for every

**φ**in C

**(**Y ).

__Every__vector v in determines a

**linear**

__map__from R to taking 1 to v, which can be thought of as a Lie algebra homomorphism.

__Every__

__map__that is injective, continuous and either open

**or**closed is an embedding ; however there are also embeddings which are neither open nor closed.

__Every__inner automorphism is indeed an automorphism of

**the**group G, i. e. it is a bijective

__map__from G to G and it is a homomorphism ; meaning

**(**xy )< sup > a </ sup >

__Every__algebraic curve C of genus g ≥ 1 is associated with an abelian variety J of dimension g, by means of an analytic

__map__of C into J.

__Every__covering

__map__is a semicovering, but semicoverings satisfy

**the**" 2 out of 3 " rule

**:**given a composition of

**maps**of

**spaces**, if two of

**the**

**maps**are semicoverings, then so also is

**the**third.

* 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__issue of our periodical will therefore include one

**or**more

__map__supplements, and their design will guarantee a continuous and easily accessible supplement in easy-to-manage form with special regard for those who own Stielers Hand-Atlas, Berghaus ’ s Physical Atlas, and other

__map__publications of

**the**

**(**Perthes

**)**Institute.

__Every__summer,

**the**town prepares for

**the**one-week summer festival, " Finnsnes i Fest ", aiming to put Finnsnes on

**the**

__map__.

__Every__element x of G gives rise to a tensor-preserving self-conjugate

**natural**transformation via multiplication by x on each representation, and hence one has a

__map__.

Every and φ

A substructure

**N**of**M**is elementary if and only if it passes**the**Tarski – Vaught test**:**__Every__first-order formula__φ__**(**x, b < sub > 1 </ sub >, …, b < sub > n </ sub >) with parameters in**N**that has a solution in**M**also has a solution in**N**when evaluated in**M**. One can prove that two structures are elementary equivalent with**the**Ehrenfeucht – Fraïssé games.__Every__arithmetical set is implicitly arithmetical ; if X is arithmetically defined by

__φ__

**(**n

**)**then it is implicitly defined by

**the**formula

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__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__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__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.1.447 seconds.