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Every hyperbolic Riemann surface has a non-trivial fundamental group.
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Every and hyperbolic
* Every triangle group T is a discrete subgroup of the isometry group of the sphere ( when T is finite ), the Euclidean plane ( when T has a Z + Z subgroup of finite index ), or the hyperbolic plane.
* Every non-split, prime, alternating link that is not a torus link is hyperbolic by a result of William Menasco.
Every complete, connected, simply-connected manifold of constant negative curvature − 1 is isometric to the real hyperbolic space H < sup > n </ sup >.
Every and Riemann
Every Riemann surface is a two-dimensional real analytic manifold ( i. e., a surface ), but it contains more structure ( specifically a complex structure ) which is needed for the unambiguous definition of holomorphic functions.
Every Riemann surface is the quotient of a free, proper and holomorphic action of a discrete group on its universal covering and this universal covering is holomorphically isomorphic ( one also says: " conformally equivalent ") to one of the following:
Every Möbius transformation is a bijective conformal map of the Riemann sphere to itself.
# Every Riemannian metric on a Riemann surface is Kähler, since the condition for ω to be closed is trivial in 2 ( real ) dimensions.
Every finite group is a subgroup of the mapping class group of a closed, orientable surface, moreover one can realize any finite group as the group of isometries of some compact Riemann surface.
) Every time we are computing a Riemann sum, we are using a particular instantiation of the integrator.
Every and surface
Every form is the delimitation of a surface by another one ; it possesses an inner content, the effect it produces on one who looks at it attentively.
Every aspect of the store is mapped out and attention is paid to colour, wording and even surface texture.
Every gland is formed by an ingrowth from an epithelial surface.
Every antiseptic, however good, is more or less toxic and irritating to a wounded surface ; as a result, in surgery, the antiseptic method has been replaced by aseptic method, which is preventative in nature and relies on keeping free from the invasion of bacteria rather than destroying them when present.
# Every K3 surface is Kähler ( by a theorem of Y .- T. Siu ).
Every smooth surface S has a unique affine plane tangent to it at each point.
Every now and then, the surface water sloshes back across the ocean, bringing warm water temperatures along the eastern coasts of the pacific.
Every such black body emits from its surface with a spectral radiance that Kirchhoff labeled ( for specific intensity, the traditional name for spectral radiance ).
Every 17 years, Brood X cicadas tunnel en masse to the surface of the ground, lay eggs, and then die off in several weeks.
Every minimal projective ruled surface other than the projective plane is the projective bundle of a 2-dimensional vector bundle over some curve.
Every conic surface is ruled and developable.
Every vehicle function that changes direction or speed relies on friction between the tires and the road surface.
Every single object or point is dwarfed ; the valley of the Hudson is only a wrinkle in the earth's surface.
Every surface of the vaulted ceiling is occupied with preserved fishes, stuffed mammals and curious shells, with a stuffed crocodile suspended in the centre.
Every integer 2g ' 2g matrix with < sup >*</ sup > arises as the Seifert matrix of a knot with genus g Seifert surface.
Every morning before sunrise, the floor of the owners house, or where ever it may be, is cleaned with water and the muddy floor is swept well for an even surface.
According to Dale E. Dawkins, AMC's vice-president, " Every square inch of inner surface on exterior body panels is galvanized on our Spirit, Concord, and Eagle models.
Every particular finite line, surface, or solid which may possibly be the object of our thought is an idea existing only in the mind, and consequently each part of it must be perceived.
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.
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