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 entire function can be represented as a power series that converges uniformly on compact sets.

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

Every special uniformly continuous real-valued function defined on the metric space is uniformly approximable by means of Lipschitz functions.

Every experiment in such a free-falling environment has the same results as it would for an observer at rest or moving uniformly in deep space, far from all sources of gravity.

# Every net on X has a convergent subnet ( see the article on nets for a proof ).

# Every filter on X has a convergent refinement.

# Every sequence in A has a convergent subsequence, whose limit lies in A.

* Sequentially compact: Every sequence has a convergent subsequence.

Every absolutely convergent series is unconditionally convergent, but the converse implication does not hold in general.

Every sequence that ran off to infinity in the real line will then converge to ∞ in this compactification.

Every sequence can, thus, be read in three reading frames, each of which will produce a different amino acid sequence ( in the given example, Gly-Lys-Pro, Gly-Asn, or Glu-Thr, respectively ).

Every page starts with the four ASCII character sequence OggS.

Lemma: Every sequence

Every synset contains a group of synonymous words or collocations ( a collocation is a sequence of words that go together to form a specific meaning, such as " car pool "); different senses of a word are in different synsets.

Every gap sequence that contains 1 yields a correct sort ; however, the properties of thus obtained versions of Shellsort may be very different.

Every variable X < sub > i </ sub > in the sequence is associated with a Bernoulli trial or experiment.

Every short exact sequence

Every sequence in principle has a generating function of each type ( except that Lambert and Dirichlet series require indices to start at 1 rather than 0 ), but the ease with which they can be handled may differ considerably.

Every time he is thrown out of the house, he is shown wearing the same shirt although he does not always wear it when he is thrown out ( the producers never shot a second sequence with Jazz being thrown out of the house, only adjusting the original scene for time purposes ; an exception is in the episode " Community Action ", where Jazz was thrown out along with a lifesize cardboard cut-out of Bill Cosby, complete with a blooper showing Jeff Townes reshooting his flying off the house several times ).

Every delta operator ' has a unique sequence of " basic polynomials ", a polynomial sequence defined by three conditions:

Every year, in numerical sequence starting from 2007-07-07 and continuing through 2012-12-12 hoopers dance in every city and country to raise money and donate hoops to others who can't afford them.

For example, to study the theorem “ Every bounded sequence of real numbers has a supremum ” it is necessary to use a base system which can speak of real numbers and sequences of real numbers.

* Every Jacobi-like polynomial sequence can have its domain shifted and / or scaled so that its interval of orthogonality is, and has Q

* Every Laguerre-like polynomial sequence can have its domain shifted, scaled, and / or reflected so that its interval of orthogonality is, and has Q =

* Every Hermite-like polynomial sequence can have its domain shifted and / or scaled so that its interval of orthogonality is, and has Q

Every Turán graph is a cograph ; that is, it can be formed from individual vertices by a sequence of disjoint union and complement operations.

* Metroid: Every game in the Metroid series has ended with either a timed self-destruct escape sequence, or a cut-scene showing the area explode, with the exception of Metroid 2.

:# Every element of D is the least upper bound of a countable increasing sequence of isolated elements.

* Conway's cosmological theorem: Every sequence eventually splits into a sequence of " atomic elements ", which are finite subsequences that never again interact with their neighbors.

* Pseudocompact: Every real-valued continuous function on the space is bounded.

* Every separable metric space is isometric to a subset of the ( non-separable ) Banach space l < sup >∞</ sup > of all bounded real sequences with the supremum norm ; this is known as the Fréchet embedding.

Every finite or bounded interval of the real numbers that contains an infinite number of points must have at least one point of accumulation.

* Every totally ordered set that is a bounded lattice is also a Heyting algebra, where is equal to when, and 1 otherwise.

* Every continuous function f: → R is bounded.

This is really a special case of a more general fact: Every continuous function from a compact space into a metric space is bounded.

Every maximal outerplanar graph with n vertices has exactly 2n − 3 edges, and every bounded face of a maximal outerplanar graph is a triangle.

Every three years the Company makes an award to the three buildings or structures, in the area bounded by the M25 motorway, which respectively embody the most outstanding example of brickwork, of slated or tiled roof and of hard-surface tiled wall and / or floor.

Every Polish town was bounded to put up a quantity of soldiers-this was a conspicuous sign of a power of a given town how much soldiers it had to put up.

Every complete lattice is also a bounded lattice, which is to say that it has a greatest and least element.

Every bounded linear transformation from a normed vector space to a complete, normed vector space can be uniquely extended to a bounded linear transformation from the completion of to.

Every bounded positive-definite measure μ on G satisfies μ ( 1 ) ≥ 0. improved this criterion by showing that it is sufficient to ask that, for every continuous positive-definite compactly supported function f on G, the function Δ < sup >– ½ </ sup > f has non-negative integral with respect to Haar measure, where Δ denotes the modular function.

Every subset of a totally bounded space is a totally bounded set ; but even if a space is not totally bounded, some of its subsets still will be.

* Every compact set is totally bounded, whenever the concept is defined.

* Every totally bounded metric space is bounded.

Every compact metric space is totally bounded.

* Every finite set of points is bounded

* Every relatively compact set in a topological vector space is bounded.

Every topological vector space X gives a bornology on X by defining a subset to be bounded iff for all open sets containing zero there exists a with.

Every ( bounded ) convex polytope is the image of a simplex, as every point is a convex combination of the ( finitely many ) vertices.