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Every 3-manifold has many embedded 2-spheres, and a 2-sphere embedded in a 3-manifold never has a compressing disc.
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Every and 3-manifold
Every closed 3-manifold has a prime decomposition: this means it is the connected sum of prime three-manifolds ( this decomposition is essentially unique except for a small problem in the case of non-orientable manifolds ).
: Every oriented prime closed 3-manifold can be cut along tori, so that the interior of each of the resulting manifolds has a geometric structure with finite volume.
* Moise's theorem – Every 3-manifold has a triangulation, unique up to common subdivision
Every closed, orientable, connected 3-manifold is obtained by performing Dehn surgery on a link in the 3-sphere.
Every and has
Every soldier in the army has, somewhere, relatives who are close to starvation.
Every woman has had the experience of saying no when she meant yes, and saying yes when she meant no.
Every detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he is playing with Viennese musicians ), and the gossamer shading throughout.
Every calculation has been made independently by two workers and checked by one of the editors.
Every retiring person has a different situation facing him.
Every family of Riviera Presbyterian Church has been asked to read the Bible and pray together daily during National Christian Family Week and to undertake one project in which all members of the family participate.
Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.
`` Every woman in the block has tried that ''.
: 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.
** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.
The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.
** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.
** Antichain principle: Every partially ordered set has a maximal antichain.
** Every vector space has a basis.
* Every small category has a skeleton.
* 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 field has an algebraic closure.
** Every field extension has a transcendence basis.
** Every Tychonoff space has a Stone – Čech compactification.
* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =
Every unit of length has a corresponding unit of area, namely the area of a square with the given side length.
Every field has an algebraic extension which is algebraically closed ( called its algebraic closure ), but proving this in general requires some form of the axiom of choice.
Every ATM cell has an 8-or 12-bit Virtual Path Identifier ( VPI ) and 16-bit Virtual Channel Identifier ( VCI ) pair defined in its header.
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 product of ( arbitrarily many ) profinite groups is profinite ; the topology arising from the profiniteness agrees with the product topology.
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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