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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 ).

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## Some Related Sentences

Every and continuous

*

__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__character is automatically

__continuous__from A to

**C**, since

**the**kernel of a character is a maximal ideal, which is closed.

*

__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__contraction mapping is Lipschitz

__continuous__and hence uniformly

__continuous__

**(**

**for**a Lipschitz

__continuous__function,

**the**constant k is no longer necessarily less than 1

**).**

*

__Every__separable metric space is isometric to a subset of**C**(),**the**separable Banach space of__continuous__functions**→**R, with**the**supremum norm.__Every__topological group can be viewed as a uniform space

**in**two ways ;

**the**left uniformity turns all left multiplications into uniformly

__continuous__maps while

**the**right uniformity turns all right multiplications into uniformly

__continuous__maps.

__Every__

__continuous__function

**in**

**the**function space can be represented as a linear combination of basis functions, just as

**every**vector

**in**a vector space can be represented as a linear combination of basis vectors.

__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__compact Hausdorff space of weight at most**(**see Aleph number**)**is**the**__continuous__image of**(**this does not need**the**continuum hypothesis, but is less interesting**in**its absence**).**__Every__place south of

**the**Antarctic Circle experiences a period of twenty-four hours '

__continuous__daylight at least once per year, and a period of twenty-four hours '

__continuous__night time at least once per year.

Every and map

__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__smooth

**(**or differentiable

**)**

__map__

**φ**

**:**M

**→**N between smooth

**(**or differentiable

**)**manifolds

**induces**natural linear maps between

**the**corresponding tangent spaces

**:**

__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.

*

__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.
* 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 f

__Every__

**homomorphism**

__f__

**:**G

**→**H of Lie groups

**induces**a

**homomorphism**between

**the**corresponding Lie algebras and.

__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__empty function is constant, vacuously, since there are no x and y

**in**A

**for**which

__f__

**(**x

**)**and

__f__

**(**y

**)**are different when A is

**the**empty set.

__Every__bounded positive-definite measure μ on G satisfies μ

**(**1

**)**≥ 0. improved this criterion

**by**showing that it is sufficient to ask that,

**for**

**every**

**continuous**positive-definite compactly supported function

__f__on G,

**the**function Δ < sup >– ½ </ sup >

__f__has non-negative integral with respect to Haar measure, where Δ denotes

**the**modular function.

__Every__morphism

__f__

**:**G

**→**H

**in**Grp has a category-theoretic kernel

**(**given

**by**

**the**ordinary kernel of

**algebra**ker

__f__

**=**

__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__solution of

**the**second half g of

**the**equation defines a unique direction

**for**x via

**the**first half

__f__of

**the**equations, while

**the**direction

**for**y is arbitrary.

__Every__deterministic complexity class

**(**DSPACE

**(**

__f__

**(**n )), DTIME

**(**

__f__

**(**n ))

**for**all

__f__

**(**n )) is closed under complement, because one can simply add a last step to

**the**algorithm which reverses

**the**answer.

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