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* Every product of ( arbitrarily many ) profinite groups is profinite ; the topology arising from the profiniteness agrees with the product topology.
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Every and product
Every Hilbert space X is a Banach space because, by definition, a Hilbert space is complete with respect to the norm associated with its inner product, where a norm and an inner product are said to be associated if for all x ∈ X.
Every positive integer n > 1 can be represented in exactly one way as a product of prime powers:
* 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 product is perfectly homogeneous and a perfect substitute for any other.
Every man-made product is composed of natural resources ( at its fundamental level ).
Every software product has a target audience.
Every data source has a different data-access language ( or API ), driving up the costs to learn and use each vendor's product.
Every scene, every shot is the product of a keen and sensitive eye — an eye which has deep comprehension of the beauty of rugged people and a rugged world ".
Every composite number can be written as the product of two or more ( not necessarily distinct ) primes ; furthermore, this representation is unique up to the order of the factors.
Every quadratic space is also an inner product space ( see below ).
Every third weekend in September Silver Creek hosts a Festival of Grapes to honor Concord grapes, an important agricultural product.
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 finite-dimensional inner product space has an orthonormal basis, which may be obtained from an arbitrary basis using the Gram – Schmidt process.
One drug company product manager has been quoted as saying, " Every marketer's dream is to find an unidentified or unknown market and develop it.
Every element in O ( 1, 3 ) can be written as the semidirect product of a proper, orthochronous transformation and an element of the discrete group
: Every product is subject to a life-cycle including a growth phase followed by a maturity phase and finally an eventual period of decline as sales falls.
* Every totally disconnected compact metric space is homeomorphic to a subset of a countable product of discrete spaces.
Every reactant in a spontaneous process has a tendency to form the corresponding product.
It is usually presented as sales minus sales discounts, returns, and allowances. Every time a business sells a product or performs a service, it obtains revenue.
Every reduced word is an alternating product of elements of G and elements of H, e. g.
* Every commutative semisimple ring must be a finite direct product of fields.
Every and arbitrarily
Every field and every polynomial ring over a field ( in arbitrarily many variables ) is a reduced ring.
Every and many
Every pitch in the game brought forth a howl from the enraptured audience and every fly ball the visitors dropped ( and because their right fielder was still a little fuzzy from drink, they dropped many ) called forth yelps of derision.
Every year many teams from all over Asia converge in Tokyo to compete.
According to Every, one example may be " the myth of St. George " and other stories about saints battling dragons, which were " modelled no doubt in many cases on older representations of the creator and preserver of the world in combat with chaos ".
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.
Cantor points out that his constructions prove more — namely, they provide a new proof of Liouville's theorem: Every interval contains infinitely many transcendental numbers.
Every Andalusian region or comarca has its own variety of this popular food so there are many types of gazpacho.
A Girl in Every Port is considered by film scholars to be the most important film of Hawks's silent career because it is his first film to introduce many of the Hawksian themes and characters that would continue until his final films.
Hilbert's example: " the assertion that either there are only finitely many prime numbers or there are infinitely many " ( quoted in Davis 2000: 97 ); and Brouwer's: " Every mathematical species is either finite or infinite.
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 linguistic act involves choice, and choices are made on many scales.
This problem is encapsulated in the phrase " Every selection of one is a rejection of many ".
Every year, many tons of salts reportedly are carried as far as 800 kilometers away.
Earlier books such as What Every Girl Should Know ( Margaret Sanger, 1920 ) and A Marriage Manual ( Hannah and Abraham Stone, 1939 ) had broken the silence in which many people, women in particular, had grown up in.
Every Saturday morning it hosts a large outdoor market or " mercadillo ", where many gypsies come and sell their wares of fruits and vegetables, clothes and shoes, and other odds and ends.
: Every integer which can be written as the sum of two primes, can also be written as the sum of as many primes as one wishes, until all terms are units.
Every tree with only countably many vertices is a planar graph.
* Every connected graph with only countably many vertices admits a normal spanning tree.
Every compact Hausdorff space is also locally compact, and many examples of compact spaces may be found in the article compact space.
Every subset of a nowhere dense set is nowhere dense, and the union of finitely many nowhere dense sets is nowhere dense.
Every monad arises from some adjunction — in fact, typically from many adjunctions — in the above fashion.
Every time, there will be many famous singers who perform on the stage that is set up for the New Year Celebration.
Every pre-abelian category is of course an additive category, and many basic properties of these categories are described under that subject.
Every two years, the museum hosts the Whitney Biennial, an international art show which displays many lesser-known artists new to the American art scene.
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