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Page "Lipschitz continuity" ¶ 37
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Every and Lipschitz
Every contraction mapping is Lipschitz continuous and hence uniformly continuous ( for a Lipschitz continuous function, the constant k is no longer necessarily less than 1 ).
Every special uniformly continuous real-valued function defined on the metric space is uniformly approximable by means of Lipschitz functions.

Every and continuous
* 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 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.
* Pseudocompact: Every real-valued continuous function on the space is bounded.
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 space filling curve hits some points multiple times, and does not have a continuous inverse.
* Every separable metric space is isometric to a subset of C (), the separable Banach space of continuous functions → R, with the supremum norm.
Every uniformly continuous function between metric spaces is continuous.
Every continuous function on a compact set is uniformly continuous.
Every topological group can be viewed as a uniform space in two ways ; the left uniformity turns all left multiplications into uniformly continuous maps while the right uniformity turns all right multiplications into uniformly continuous maps.
Every continuous function in the function space can be represented as a linear combination of basis functions, just as every vector in a vector space can be represented as a linear combination of basis vectors.
Every embedding is injective and continuous.
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 compact Hausdorff space of weight at most ( see Aleph number ) is the continuous image of ( this does not need the continuum hypothesis, but is less interesting in its absence ).
Every place south of the Antarctic Circle experiences a period of twenty-four hours ' continuous daylight at least once per year, and a period of twenty-four hours ' continuous night time at least once per year.

Every and map
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 smooth ( or differentiable ) map φ: M → N between smooth ( or differentiable ) manifolds induces natural linear maps between the corresponding tangent spaces:
Every distinct map projection distorts in a distinct way.
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 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 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 and is
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.

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