Any normal subgroup has a corresponding quotient group, formed from the larger group by eliminating the distinction between elements of the subgroup.

Any quotient of a ring by a maximal ideal is a simple ring.

Any such surface is the Kummer variety of the Jacobian of a smooth hyperelliptic curve of genus 2 ; i. e. a quotient of the Jacobian by the Kummer involution x ↦ − x.

* Any irreducible representation R of H gives an irreducible representation of G using the quotient map from G to H ( that is, as a restricted representation ).

Any quotient group of a group with property FA has property FA.

* Any subspace and any quotient space by a closed subspace of a nuclear space is nuclear.

* Any open subset of a finite-dimensional real, and therefore complex, vector space is a diffeological space.

* Any smooth manifold is a diffeological space.

* Any finite topological space, including the empty set, is compact.

* Any space carrying the cofinite topology is compact.

* Any locally compact Hausdorff space can be turned into a compact space by adding a single point to it, by means of Alexandroff one-point compactification.

Any field may be used as the scalars for a vector space, which is the standard general context for linear algebra.

Any disturbance created in a sufficiently small region of isotropic space ( or in an isotropic medium ) propagates from that region in all radial directions.

Any major failure to a spacecraft en route is likely to be fatal, and even a minor one could have dangerous results if not repaired quickly, something difficult to accomplish in open space.

* Any vector space V endowed with the identically zero Lie bracket becomes a Lie algebra.

Any object gravitationally held by the rotating Earth – Moon system will be attracted to the barycenter to an equal and opposite degree as its tendency to fly off into space.

Any fire in a crew space will be automatically extinguished with Halon or another fire suppressant.

Any topological space which is itself finite or countably infinite is separable, for the whole space is a countable dense subset of itself.

Any second-countable space is separable: if is a countable base, choosing any gives a countable dense subset.

* Any continuous image of a separable space is separable.

* Any topological space which is the union of a countable number of separable subspaces is separable.

Any brain tumor is inherently serious and life-threatening because of its invasive and infiltrative character in the limited space of the intracranial cavity.

Any conformal map on a portion of Euclidean space of dimension greater than 2 can be composed from three types of transformation: a homothetic transformation, an isometry, and a special conformal transformation.

Any number of playing pieces may occupy the same space at the same time.

# Any phenomena that would seem attributable to absolute space and time ( e. g. inertia, and centrifugal force ) should instead be seen as emerging from the large scale distribution of matter in the universe.

* Any topological space can be viewed as a category by taking the open sets as objects, and a single morphism between two open sets and if and only if.

Any relatively flat, open space can be used as a terrain.

Any attempt to contact other worlds was forbidden, and the planetary government maintained an isolationist stance, forbidding space exploration of any kind.

Any competitor may rent office space in an incumbent's central office, place equipment to interconnect with their network, or purchase other related services.

Any organism that falters or misperceives the signals or weakens is done.

Any information we have here in Taiwan is at your disposal ''.

Any claimant whose claim is denied, or is approved for less than the full amount of such claim, shall be entitled, under such regulations as the Commission may prescribe, to a hearing before the Commission, or its duly authorized representatives, with respect to such claim.

Any alteration of one of these factors is distortion, although we generally use that word only for effects so pronounced that they can be stated quantitatively on the basis of standard tests.

Any musician playing Beethoven here, where Beethoven was born, is likely to examine his own interpretations with special care.

Any action is understood to create " seeds " in the mind that sprout into the appropriate results ( Pāli vipaka ) when they meet the right conditions.

** Any union of countably many countable sets is itself countable.

Any information may be conveyed by an analog signal ; often such a signal is a measured response to changes in physical phenomena, such as sound, light, temperature, position, or pressure.

Any quantity of energy absorbed by the electron in excess of this amount is converted to kinetic energy according to the conservation of energy.

Any breach of these laws is a criminal offence and can lead to fine of up to £ 5, 000 or six months in prison.

The prohibition against retaliation or coercion applies broadly to any individual or entity that seeks to prevent an individual from exercising his or her rights or to retaliate against him or her for having exercised those rights ... Any form of retaliation or coercion, including threats, intimidation, or interference, is prohibited if it is intended to interfere.

Any word or phrase that exactly reproduces the letters in another order is an anagram.

Any work ( δW ) done must be done at the expense of internal energy U, since no heat δQ is being supplied from the surroundings.

" Any threat of war Clovis could make would only be effective if they were neighbors ; " it is nowhere written that Syagrius was handed over in 486 or 487.

Any player may declare the game over at any time during his turn if either of two conditions is true: one chain has 41 or more tiles, or there is at least one chain on the board and every chain on the board has 11 or more tiles.

Any person who is seen as a threat to civil aviation is banned from flying.

* Any ring of characteristic n is a ( Z / nZ )- algebra in the same way.

* Any ring A is an algebra over its center Z ( A ), or over any subring of its center.

* Any commutative ring R is an algebra over itself, or any subring of R.

Any form of intelligent life would do ; so, specifying carbon-based life, per se, is irrelevant.

* Any base that is water-soluble and forms hydroxide ions or the solution of a base in water.