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 closed smooth 4-manifold is a union of two Stein 4-manifolds glued along their common boundary.

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 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 continuous map f: X → Y induces an algebra homomorphism C ( f ): C ( Y ) → C ( X ) by the rule C ( f )( φ ) = φ o f for every φ in C ( Y ).

Every vector v in determines a linear map from R to taking 1 to v, which can be thought of as a Lie algebra homomorphism.

* Every Lipschitz continuous map is uniformly continuous, and hence a fortiori continuous.

Every distinct map projection distorts in a distinct way.

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 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 constant map is a plot.

Every regular map of varieties is continuous in the Zariski topology.

Every real m-by-n matrix yields a linear map from R < sup > n </ sup > to R < sup > m </ sup >.

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 local homeomorphism is a continuous and open map.

Every covering map is a semicovering, but semicoverings satisfy the " 2 out of 3 " rule: given a composition of maps of spaces, if two of the maps are semicoverings, then so also is the third.

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

* The embedding theorem for Stein manifolds states the following: Every Stein manifold of complex dimension can be embedded into by a biholomorphic proper map.

Every issue of our periodical will therefore include one or more map supplements, and their design will guarantee a continuous and easily accessible supplement in easy-to-manage form with special regard for those who own Stielers Hand-Atlas, Berghaus ’ s Physical Atlas, and other map publications of the ( Perthes ) Institute.

Every map consists of numerous textured polygons carefully positioned in relation to one another.

Every summer, the town prepares for the one-week summer festival, " Finnsnes i Fest ", aiming to put Finnsnes on the map.

* Every map can be replaced by a cofibration via the mapping cylinder construction

* Every local diffeomorphism is also a local homeomorphism and therefore an open map.

Every element x of G gives rise to a tensor-preserving self-conjugate natural transformation via multiplication by x on each representation, and hence one has a map.

Every map has these two bases, but each map has a different pattern of fixed terrain features.

Every rotation Rot ( φ ) has an inverse Rot (− φ ).

A substructure N of M is elementary if and only if it passes the Tarski – Vaught test: Every first-order formula φ ( x, b < sub > 1 </ sub >, …, b < sub > n </ sub >) with parameters in N that has a solution in M also has a solution in N when evaluated in M. One can prove that two structures are elementary equivalent with the Ehrenfeucht – Fraïssé games.

Every arithmetical set is implicitly arithmetical ; if X is arithmetically defined by φ ( n ) then it is implicitly defined by the formula

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

Every song they wrote was written with an eye toward giving it " deep hidden meaning " or D. H. M.

* In any ring R, a maximal ideal is an ideal M that is maximal in the set of all proper ideals of R, i. e. M is contained in exactly 2 ideals of R, namely M itself and the entire ring R. Every maximal ideal is in fact prime.

Every measurable cardinal κ is a 0-huge cardinal because < sup > κ </ sup > M ⊂ M, that is, every function from κ to M is in M. Consequently, V < sub > κ + 1 </ sub >⊂ M.

# " 5. 06 A. M. ( Every Strangers ' Eyes )"

: Every countable theory which is satisfiable in a model M, is satisfiable in a countable substructure of M.

* Siegal, M., Cornell Feline Health Center ( Editors ) ( 1989 ) The Cornell Book of Cats: A Comprehensive Medical Reference for Every Cat and Kitten.

* Every endomorphism of M is either nilpotent or invertible.

Every year about 5000 applications are received, out of which about 300 students ( around 150 in each year ) are enrolled in the 2 year full time M. Tech.

Every hyperkähler manifold M has a 2-sphere of complex structures ( i. e. integrable almost complex structures ) with respect to which the metric is Kähler.

* Every module M has an injective hull.

Every finite-length module M has a composition series, and the length of every such composition series is equal to the length of M.

Every year the department admits students for it M. A / MSc., M. Phil and Ph. D courses.

* Every direct summand of M is pure in M. Consequently, every subspace of a vector space over a field is pure.