Every time I closed my eyes, I saw Gray Eyes rushing at me with a knife.

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 unital real Banach algebra with no zero divisors, and in which every principal ideal is closed, is isomorphic to the reals, the complexes, or the quaternions.

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 closed subgroup of a profinite group is itself profinite ; the topology arising from the profiniteness agrees with the subspace topology.

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

* Every closed nowhere dense set is the boundary of an open set.

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 base he closed resulted in a new construction project elsewhere to expand another base, relocation of forces projects and other related spending.

Every year the central business district ( with corners at the Municipal Building, Grand Street Fire House and Croton-Harmon High School ) is closed to automobile traffic for music, American food, local fund raisers, traveling, and local artists.

The generalized Poincaré conjecture states that Every simply connected, closed n-manifold is homeomorphic to the n-sphere.

Every closed subspace of a reflexive space is reflexive.

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.

* Every integrable subbundle of the tangent bundle — that is, one whose sections are closed under the Lie bracket — also defines a Lie algebroid.

* Every irreducible closed subset of P < sup > n </ sup >( k ) of codimension one is a hypersurface ; i. e., the zero set of some homogeneous polynomial.

Every October the high street is closed for the two Saturdays either side of 11 October for the Marlborough Mop Fair.

Every closed point of Hilb ( X ) corresponds to a closed subscheme of a fixed scheme X, and every closed subscheme is represented by such a point.

Every homeomorphism is open, closed, and continuous.

Every closed curve c on X is homologous to for some simple closed curves c < sub > i </ sub >, that is,

Every smooth ( or differentiable ) map φ: M → N between smooth ( or differentiable ) manifolds induces natural linear maps between the corresponding tangent spaces:

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 smooth manifold defined in this way has a natural diffeology, for which the plots correspond to the smooth maps from open subsets of R < sup > n </ sup > to the manifold.

Every smooth function G over the symplectic manifold generates a one-parameter family of symplectomorphisms and if

* Every bundle of Lie algebras over a smooth manifold defines a Lie algebroid where the Lie bracket is defined pointwise and the anchor map is equal to zero.

Every smooth surface S has a unique affine plane tangent to it at each point.

Every Sámi settlement had its seita, which had no regular shape, and might consist of smooth or odd-looking stones picked out of a stream, of a small pile of stones, of a tree-stump, or of a simple post.

Every compact smooth manifold of dimension 2n, which has only handles of index ≤ n, has a Stein structure provided n > 2, and when n = 2 the same holds provided the 2-handles are attached with certain framings ( framing less than the Thurston-Bennequin framing ).

Every sufficiently smooth DAE is almost everywhere reducible to this semi-explicit index-1 form.

* Every smooth Hilbert manifold can be smoothly embedded onto an open subset of the model Hilbert space.

* Every continuous plurisubharmonic function can be obtained as a limit of monotonically decreasing sequence of smooth plurisubharmonic functions.

Every camp has one or two directors ; the job of the director is to make the camp run smooth and mostly safe without losing the free-spirited and cosy experience of the camp.

Every legislator from Brasstown Bald to Folkston is going to have his every vote subjected to the closest scrutiny as a test of his political allegiances, not his convictions.

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 taxpayer is well aware of the vast size of our annual defense budget and most of our readers also realize that a large portion of these expenditures go for military electronics.

Every single problem touched on thus far is related to good marketing planning.

Every few days, in the early morning, as the work progressed, twenty men would appear to push it ahead and to shift the plank foundation that distributed its weight widely on the Rotunda pavement, supported as it is by ancient brick vaulting.

Every dream, and this is true of a mental image of any type even though it may be readily interpreted into its equivalent of wakeful thought, is a psychic phenomenon for which no explanation is available.

Every man in every one of these houses is a Night Rider.

Every library borrower, or at least those whose taste goes beyond the five-cent fiction rentals, knows what it is to hear the librarian say apologetically, `` I'm sorry, but we don't have that book.

Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.

The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.

** Every infinite game in which is a Borel subset of Baire space is determined.

Every natural-born citizen of a foreign state who is also an American citizen and every natural-born American citizen who is a citizen of a foreign land owes a double allegiance, one to the United States, and one to his homeland ( in the event of an immigrant becoming a citizen of the US ), or to his adopted land ( in the event of an emigrant natural born citizen of the US becoming a citizen of another nation ).

Every line of written text is a mere reflection of references from any of a multitude of traditions, or, as Barthes puts it, " the text is a tissue of quotations drawn from the innumerable centres of culture "; it is never original.

Every root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.

* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =

Every year, on the last Sunday in April, there is an ice fishing competition in the frozen estuarine waters of the Anadyr River's mouth.

Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping.