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 finite-dimensional normed space is reflexive, simply because in this case, the space, its dual and bidual all have the same linear dimension, hence the linear injection J from the definition is bijective, by the rank-nullity theorem.

Every finite-dimensional Hausdorff topological vector space is reflexive, because J is bijective by linear algebra, and because there is a unique Hausdorff vector space topology on a finite dimensional vector space.

Every Möbius transformation is a bijective conformal map of the Riemann sphere to itself.

: Every set has a choice 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 surjective function has a right inverse.

* Pseudocompact: Every real-valued continuous function on the space is bounded.

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 effectively calculable function is a computable function.

Every effectively calculable function ( effectively decidable predicate ) is general recursive italics

Every effectively calculable function ( effectively decidable predicate ) is general recursive.

Every entire function can be represented as a power series that converges uniformly on compact sets.

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 holomorphic function is analytic.

Every completely multiplicative function is a homomorphism of monoids and is completely determined by its restriction to the prime numbers.

Every polynomial P in x corresponds to a function, ƒ ( x )

Every primitive recursive function is a general recursive function.

Every time another object or customer enters the line to wait, they join the end of the line and represent the “ enqueue ” function.

Every function is a method and methods are always called on an object.

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 uniformly continuous function between metric spaces is continuous.

Every continuous function on a compact set is uniformly continuous.

Every output of an encoder can be described by its own transfer function, which is closely related to the generator polynomial.

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 tile belongs to the two suits of its two values, e. g. 0 – 3 belongs both to the blank suit ( or 0 suit ) and to the 3 suit.

Every open subgroup H is also closed, since the complement of H is the open set given by the union of open sets gH for g in G

While early questions were similar to the NBC version ( e. g., " Every morning, John puts _________ on his cereal "), the questions quickly became more humorous.

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 other fret remains unaffected ( e. g. the 7th fret of an E-string will still play a B note for any capo position at or below the 7th fret ), and thus a performer does not need to adjust for or relearn the entire fretboard as they might with retuning.

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 kind of cereal and many fruits grow in great abundance, e. g. wheat, millet, barley and melons, also rice and cotton.

There are a few references to Trixie's burlesque background in the lost episodes ( e. g., Norton: " Every night I'd meet her backstage and hand her a rose ...

Every conceivable method of applying cutting fluid ( e. g., flooding, spraying, dripping, misting, brushing ) can be used, with the best choice depending on the application and the equipment available.

Every year, the five societies compete in " Society Olympics " for the famed " Pink Flamingo " trophy in a series of events ( e. g., dance-off, dodgeball, limbo contest ) that test the unorthodox talents of the students in each society.

Kant argues that there are synthetic judgments such as the connection of cause and effect ( e. g., "... Every effect has a cause.

Every reduced word is an alternating product of elements of G and elements of H, e. g.

Every highly composite number is a product of primorials ( e. g. 360 = 2 · 6 · 30 ).

: Every vessel must at all times maintain a proper look-out by sight ( day shape or lights by eyes or visual aids ) and hearing ( sound signal or Marine VHF radio ) as well as by all available means ( e. g., Radar, Automatic Radar Plotting Aid ( ARPA ), Automatic Identification System ( AIS ), GMDSS ...) in order to make a full assessment of the situation and risk of collision.

Every subsequent building took on the Crystal name ( e. g., Crystal Gateway, Crystal Towers ) and eventually the whole neighborhood.

Every function that was not assigned to a key could be invoked through the < u > XEQ </ u > key ( pronounced EXEQTE — " execute ") and spelled out in full, e. g. < u > XEQ </ u > FACT for the factorial function.

* Every character value is a sum of n m < sup > th </ sup > roots of unity, where n is the degree ( that is, the dimension of the associated vector space ) of the representation with character χ and m is the order of g. In particular, when F is the field of complex numbers, every such character value is an algebraic integer.

Every child must be insured individually maximally up to their 25th year ( e. g. if studying, if not, then earlier, regularly apprenticeship lasts 2½ – 3 years ).

Consider a Lie algebra g over a field K. Every element x of g defines the adjoint endomorphism ad ( x ) ( also written as ad < sub > x </ sub >) of g with the help of the Lie bracket, as

* Every member of the organization performs the acts we assume to constitute an expression of preference among the scheduled alternatives, e. g., voting.