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* Every finite p-local spectrum X has the property that K ( n )< sub >∗</ sub >( X ) = 0 if and only if n is less than a certain number N, called the type of the spectrum X.
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Every and finite
** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.
# Every open cover of A has a finite subcover.
* Countably compact: Every countable open cover has a finite subcover.
# Every finite and contingent being has a cause.
Every finite simple group is isomorphic to one of the following groups:
Hilbert's example: " the assertion that either there are only finitely many prime numbers or there are infinitely many " ( quoted in Davis 2000: 97 ); and Brouwer's: " Every mathematical species is either finite or infinite.
* Every finite topological space gives rise to a preorder on its points, in which x ≤ y if and only if x belongs to every neighborhood of y, and every finite preorder can be formed as the specialization preorder of a topological space in this way.
Every finite tree structure has a member that has no superior.
Every rational number / has two closely related expressions as a finite continued fraction, whose coefficients can be determined by applying the Euclidean algorithm to.
* Every finite tree with n vertices, with, has at least two terminal vertices ( leaves ).
Every finite group of exponent n with m generators is a homomorphic image of B < sub > 0 </ sub >( m, n ).
Every known Sierpinski number k has a small covering set, a finite set of primes with at least one dividing k · 2 < sup > n </ sup >+ 1 for each n > 0.
Every finite-dimensional Hausdorff topological vector space is reflexive, because J is bijective by linear algebra, and because there is a unique Hausdorff vector space topology on a finite dimensional vector space.
: 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 finite or bounded interval of the real numbers that contains an infinite number of points must have at least one point of accumulation.
Every field of either type can be realized as the field of fractions of a Dedekind domain in which every non-zero ideal is of finite index.
Every process involving charged particles emits infinitely many coherent photons of infinite wavelength, and the amplitude for emitting any finite number of photons is zero.
Every finite group has a composition series, but not every infinite group has one.
* Every finite or cofinite subset of the natural numbers is computable.
* Every subset of may be covered by a finite set of positive orthants, whose apexes all belong to
* Every finite subextension of F / k is separable.
Every finite ordinal ( natural number ) is initial, but most infinite ordinals are not initial.
* Every finite-dimensional central simple algebra over a finite field must be a matrix ring over that field.
* Every commutative semisimple ring must be a finite direct product of fields.
Every and spectrum
Every wavelength of light is perceived as a spectral color, in a continuous spectrum ; the colors of sufficiently close wavelengths are indistinguishable.
Every and X
Every Hilbert space X is a Banach space because, by definition, a Hilbert space is complete with respect to the norm associated with its inner product, where a norm and an inner product are said to be associated if for all x ∈ X.
* Every topological space X is a dense subspace of a compact space having at most one point more than X, by the Alexandroff one-point compactification.
# 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 ultrafilter on X converges to at least one point.
# Every infinite subset of X has a complete accumulation point.
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 linear combination of its components Y = a < sub > 1 </ sub > X < sub > 1 </ sub > + … + a < sub > k </ sub > X < sub > k </ sub > is normally distributed.
Every significant section of roadway maintained by the state is assigned a number, officially State Highway Route X but commonly called Route X by the NJDOT and the general public.
Every variable X < sub > i </ sub > in the sequence is associated with a Bernoulli trial or experiment.
* Every X is a Y.
Every Gauss – Markov process X ( t ) possesses the three following properties:
Every time someone gave an answer that was not on the board, the family lose a life, accompanied by a large " X " on the board with the infamous " uh-uhh " sound.
Every sigma-ideal on X can be recovered in this way by placing a suitable measure on X, although the measure may be rather pathological.
* Every non-empty Baire space is of second category in itself, and every intersection of countably many dense open subsets of X is non-empty, but the converse of neither of these is true, as is shown by the topological disjoint sum of the rationals and the unit interval 1.
* Every cover is a local homeomorphism — that is, for every, there exists a neighborhood of c and a neighborhood of such that the restriction of p to U yields a homeomorphism from U to V. This implies that C and X share all local properties.
Every universal cover p: D → X is regular, with deck transformation group being isomorphic to the fundamental group.
Every cumulant is just μ times the corresponding cumulant of the constant random variable X = 1.
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.
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