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Every uniformly continuous function between metric spaces is continuous.

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## Some Related Sentences

Every and uniformly

__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__entire

**function**can be represented as a power series that converges

__uniformly__on compact sets

**.**

__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__special

__uniformly__

**continuous**real-valued

**function**defined on the

**metric**space

**is**

__uniformly__approximable by means of Lipschitz functions

**.**

__Every__experiment in such a free-falling environment has the same results as it would for an observer at rest or moving

__uniformly__in deep space, far from all sources of gravity

**.**

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__

__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__separable**metric**space**is**isometric to a subset of C (), the separable Banach space of__continuous__functions → R, with the supremum norm**.**__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 function

__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

**.**

__Every__effectively calculable

__function__( effectively decidable predicate )

**is**general recursive italics

__Every__bijective

__function__g has an inverse g < sup >− 1 </ sup >, such that gg < sup >− 1 </ sup > = I ;

__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__completely multiplicative

__function__

**is**a homomorphism of monoids and

**is**completely determined by its restriction to the prime numbers

**.**

__Every__time another object or customer enters the line to wait, they join the end of the line and represent the “ enqueue ”

__function__

**.**

__Every__type that

**is**a member of the type class defines a

__function__that will extract the data from the string representation of the dumped data

**.**

__Every__output of an encoder can be described by its own transfer

__function__, which

**is**closely related to the generator polynomial

**.**

Every and between

__Every__morning early, in the summer, we searched the trunks of the trees as high as we could reach for the locust shells, carefully detached their hooked claws from the bark where they hung, and stabled them, a weird faery herd, in an angle

__between__the high roots of the tulip tree, where no grass grew in the dense shade

**.**

__Every__year both clubs play the " Klassieker " (" The Classic "), a derby match

__between__the teams from the two largest cities of the Netherlands

**.**

Disraeli wrote a personal letter to Gladstone, asking him to place the good of the party above personal animosity: "

__Every__man performs his office, and there**is**a Power, greater than ourselves, that disposes of all this ..." In responding to Disraeli Gladstone denied that personal feelings played any role in his decision then and previously to accept office, while acknowledging that there were differences__between__him and Derby " broader than you may have supposed**.**__Every__information exchange

__between__living organisms — i

**.**e

**.**transmission of signals that involve a living sender and receiver can be considered a form of communication ; and even primitive creatures such as corals are competent to communicate

**.**

__Every__six months the presidency rotates

__between__the states, in an order predefined by the Council's members, allowing each state to preside over the body

**.**

During the Renaissance, there arose a critical attitude that sharply distinguished

__between__apostolic tradition and what George__Every__calls " subsidiary mythology "— popular legends surrounding saints, relics, the cross, etc .— suppressing the latter**.**
George

__Every__discusses the connection__between__the cosmic center and Golgotha in his book Christian Mythology, noting that the image of Adam's skull beneath the cross appears in many medieval representations of the crucifixion**.**__Every__module over a division ring has a basis ; linear maps

__between__finite-dimensional modules over a division ring can be described by matrices, and the Gaussian elimination algorithm remains applicable

**.**

__Every__Mac made

__between__1986 and 1998 has a SCSI port on the back, making external expansion easy ; also, " toaster " Compact Macs did not have easily accessible hard drive bays ( or, in the case of the Mac Plus, any hard drive bay at all ), so on those models, external SCSI disks were the only reasonable option

**.**

__Every__two months IMU publishes an electronic newsletter, IMU-Net, that aims to improve communication

__between__IMU and the worldwide mathematical community by reporting on decisions and recommendations of the Union, major international mathematical events and developments, and on other topics of general mathematical interest

**.**

British playwright Tom Stoppard wrote

__Every__Good Boy Deserves Favour about the relationship__between__a patient and his doctor in one of these hospitals**.**__Every__citation he found described an encounter

__between__males where one party, the master, physically abused another, the slave

**.**

*

__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__homomorphism f: G → H of Lie groups induces a homomorphism

__between__the corresponding Lie algebras and

**.**

__Every__LORAN chain in the world uses a unique Group Repetition Interval, the number of which, when multiplied by ten, gives how many microseconds pass

__between__pulses from a given station in the chain

**.**

*

__Every__episode of James Joyce's modernist novel Ulysses ( 1922 ) has an assigned theme, technique and correspondences__between__its characters and those of Homer's Odyssey**.**__Every__quark in the universe does not attract every other quark in the above distance independent manner, since colour-confinement implies that the strong force acts without distance-diminishment only

__between__pairs of single quarks, and that in collections of bound quarks ( i

**.**e., hadrons ), the net colour-charge of the quarks cancels out, as seen from far away

**.**

__Every__smooth ( or differentiable ) map φ: M → N

__between__smooth ( or differentiable ) manifolds induces natural linear maps

__between__the corresponding tangent

**spaces**:

They draw three conclusions from Austin: ( 1 ) A performative utterance does not communicate information about an act second-hand — it

**is**the act ; ( 2 )__Every__aspect of language (" semantics, syntactics, or even phonematics ") functionally interacts with pragmatics ; ( 3 ) There**is**no distinction__between__language and speech**.**__Every__year the mayor and the 24 échevins would swear an oath of allegiance "

__between__the hands " of the king or his representative, usually the lieutenant général or the sénéchaussée

**.**

__Every__car uses either a 5

**.**0 L Ford " Boss 302 " SVO or a 5

**.**0 L Chevrolet small block race-engine ( depending on the make )-capable of producing

__between__460 and 485 kW ( 620 — 650 bhp ) of power, but generally quoted as a little over 450 kW ( 600 bhp ) in race trim

**.**

__Every__morphism in a concrete category whose underlying

**function**

**is**injective

**is**a monomorphism ; in other words, if morphisms are actually functions

__between__sets, then any morphism which

**is**a one-to-one

**function**will necessarily be a monomorphism in the categorical sense

**.**

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