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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 >.

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## 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__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 R

__Every__holomorphic function can be separated into its real and imaginary parts, and

**each**

**of**these

**is**a solution

**of**Laplace's equation

**on**

__R__

**<**

**sup**

**>**2

**</**

**sup**

**>.**

__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__binary relation

__R__

**on**a set S can be extended to a preorder

**on**S by taking

**the**transitive closure and reflexive closure,

__R__

**<**

**sup**>+=</

**sup**

**>.**

* 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__separable**metric****space****is**isometric to a subset**of**C (),**the**separable Banach**space****of**continuous functions →__R__, with**the**supremum norm.__Every__simple R-module

**is**isomorphic to a quotient

__R__/ m where m

**is**a maximal right ideal

**of**

__R__. By

**the**above paragraph, any quotient

__R__/ m

**is**a simple module.

__Every__random vector gives rise to a probability measure

**on**

__R__

**<**

**sup**

**>**

**n**

**</**

**sup**

**>**with

**the**Borel algebra as

**the**underlying sigma-algebra.

__Every__prime ideal P in a Boolean ring

__R__

**is**maximal

**:**

**the**quotient ring

__R__/ P

**is**

**an**integral domain and also a Boolean ring, so it

**is**isomorphic to

**the**field F

**<**sub

**>**2

**</**sub >, which shows

**the**maximality

**of**P. Since maximal ideals are always prime, prime ideals and maximal ideals coincide in Boolean rings.

*

__Every__left ideal I in__R__**is**finitely generated, i. e. there exist elements a**<**sub**>**1**</**sub >, ..., a**<**sub**>****n****</**sub**>**in I such that I = Ra**<**sub**>**1**</**sub**>**+ ... + Ra**<**sub**>****n****</**sub**>.**
*

__Every__non-empty set**of**left ideals**of**__R__, partially ordered by inclusion,**has**a maximal element with respect to set inclusion.__Every__year since 1982,

**the**W. C. Handy Music Festival

**is**held in

**the**Florence / Sheffield / Muscle Shoals area, featuring blues, jazz, country, gospel, rock music and

__R__& B.

__Every__adult citizen

**of**this small settlement signed

**the**small petition ; E. K Dyer and his wife, William Johnson, Joseph Otis and his wife, Hiram Walker and his wife, Joseph Pease and

__R__. H. Valentine.

Every and <

*

__Every__quadratic Bézier curve**is**also a cubic Bézier curve, and more generally, every degree**n**Bézier curve**is**also a degree m curve for any m**>****n**. In detail, a degree**n**curve with control points P__<__sub**>**0**</**sub >, …, P__<__sub**>****n****</**sub**>****is**equivalent ( including**the**parametrization ) to**the**degree**n**+ 1 curve with control points P '< sub**>**0**</**sub >, …, P '< sub**>****n**+ 1**</**sub >, where.__Every__bijective function

**g**

**has**

**an**inverse

**g**

__<__

**sup**>− 1

**</**

**sup**>, such that gg

__<__

**sup**>− 1

**</**

**sup**

**>**= I ;

__Every__atom across this plane

**has**

**an**individual set

**of**emission cones .</ p

**>**

__<__p

**>**Drawing

**the**billions

**of**overlapping cones

**is**impossible, so this

**is**a simplified diagram showing

**the**extents

**of**all

**the**emission cones combined.

__Every__time

**an**MTA receives

**an**email message, it adds a

__<__tt

**>**Received

**</**tt

**>**trace header field to

**the**top

**of**

**the**header

**of**

**the**message, thereby building a sequential record

**of**MTAs handling

**the**message.

*

__Every__separable**metric****space****is**isometric to a subset**of****the**( non-separable ) Banach**space**l__<__**sup**>∞</**sup****>****of**all bounded real sequences with**the**supremum norm ; this**is**known as**the**Fréchet embedding.__Every__twin prime pair except ( 3, 5 )

**is**

**of**

**the**form ( 6n − 1, 6n + 1 ) for some natural number

**n**, and with

**the**exception

**of**

__<__var

**>**

**n**

**</**var

**>**= 1,

__<__var

**>**

**n**

**</**var

**>**must end in 0, 2, 3, 5, 7, or 8.

*

__Every__linear combination**of**its components Y = a__<__sub**>**1**</**sub**>**X__<__sub**>**1**</**sub**>**+ … + a__<__sub**>**k**</**sub**>**X__<__sub**>**k**</**sub**>****is**normally distributed.__Every__sedenion

**is**a real linear combination

**of**

**the**unit sedenions 1,

__<__var

**>**e

**</**var >< sub

**>**1

**</**sub >,

__<__var

**>**e

**</**var >< sub

**>**2

**</**sub >,

__<__var

**>**e

**</**var >< sub

**>**3

**</**sub >, ..., and

__<__var

**>**e

**</**var >< sub

**>**15

**</**sub >,

Every and sup

__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__previous group 17 element

**has**seven electrons in its valence shell, forming a valence electron configuration

**of**ns

**<**

__sup__

**>**2

**</**

__sup__

**>**np

**<**

__sup__

**>**5

**</**

__sup__

**>.**

Every and >

1.421 seconds.