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Every uniformly continuous function between metric spaces is continuous.
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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.