:* Any subset of the identity relation on X has equivalence classes that are the singletons of X.

Any subset of R < sup > n </ sup > ( with its subspace topology ) that is homeomorphic to another open subset of R < sup > n </ sup > is itself open.

Any one language has only a subset of the aspectual distinctions attested in the world's languages, and some languages ( such as Standard German ; see below ) do not have aspects.

Any measurable subset of a null set is itself a null set.

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 subset of resource, but typically at least the processor state, may be associated with each of the process ' threads in operating systems that support threads or ' daughter ' processes.

Any function can be restricted to a subset of its domain.

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

Any ordinal is, of course, an open subset of any further ordinal.

* Any subset of a meagre set is meagre ; any superset of a comeagre set is comeagre.

Any discrete subset of Euclidean space is countable, since the isolation of each of its points ( together with the fact the rationals are dense in the reals ) means that it may be mapped 1-1 to a set of points with rational co-ordinates, of which there are only countably many.

Any proposed inverse R of F ( reconstruction formula, in the lingo ) would have to map to some subset of.

Any action of the group by continuous affine transformations on a compact convex subset of a ( separable ) locally convex topological vector space has a fixed point.

Any induced subgraph of a comparability graph is itself a comparability graph, formed from the restriction of the partial order to a subset of its elements.

* Any directed set A may be made into a Cauchy space by declaring a filter F to be Cauchy if, given any element n of A, there is an element U of F such that U is either a singleton or a subset of the tail

Any subset of a group closed under multiplication, under inversion and under identity ( i. e.

Any given neuron only responds to a subset of stimuli within its receptive field.

* Any open subset of an n-manifold is a n-manifold with the subspace topology.

Any set of five points in the plane in general position has a subset of four points that form the vertices of a convex quadrilateral.

Any individual has one of six possible genotypes ( AA, AO, BB, BO, AB, and OO ) that produce one of four possible phenotypes: " A " ( produced by AA homozygous and AO heterozygous genotypes ), " B " ( produced by BB homozygous and BO heterozygous genotypes ), " AB " heterozygotes, and " O " homozygotes.

Brown continued releasing recordings: in 1993, he issued the album, Universal James, which included Brown's final Billboard charted single, " Can't Get Any Harder ", which peaked at # 76 on the US R & B chart and # 59 on the UK chart.

The blitter's block copying mode takes zero to three data sources in memory, called A, B and C, performs a programmable boolean function on the data sources and writes the result to a destination area, D. Any of these four areas can overlap.

Any such function is called a Urysohn function for A and B.

Any member of B is in the set ker r + im u ; since for all b in B, b =

Any attempts to make this schedule serial would give off two different results ( either T1's version of A / B is shown, or T2's version of A and B is shown ), and would not be the same as the above schedule.

Any prospect for further mining of the lead-zinc resource would now require significant investment to bring in mining equipment, and it would need to come entirely by road unless a B. C .- Alaska railway is built or the White Pass route is reopened to freight traffic to Whitehorse.

Gates 20-28 are swing gates between Concourse B and C. Any US bound flight is treated as a " C " Gate, whereas any Canadian-bound / International-bound flight is treated as a " B " Gate.

Robert Christgau's review of Into the Unknown was more favorable than that of How Could Hell Be Any Worse ?, which received a B rating, whereas Into the Unknown was given a A-rating.

Any ring homomorphism A → B gives a map K < sub > 0 </ sub >( A ) → K < sub > 0 </ sub >( B ) by mapping ( the class of ) a projective A-module M to M ⊗< sub > A </ sub > B, making K < sub > 0 </ sub > a covariant functor.

In early June, Banks released the second single off the album, " Any Girl " featuring R & B singer Lloyd.

Any pa ( or sentential logic ) formula B can be viewed as an ordered tree with branches.

# Any three points A, B, C of a plane α, which do not lie in the same straight line, completely determine that plane.

Any four points A, B, C, D of a straight line can always be so arranged that B shall lie between A and C and also between A and D, and, furthermore, that C shall lie between A and D and also between B and D.

Any genus zero handlebody is homeomorphic to the three-ball B < sup > 3 </ sup >.

( B ) RISK ATTRIBUTABLE TO FAULT OF EITHER PARTY: Any damage or loss which arises as a result of the fault or neglect of the seller or the buyer or their respective agents as the case may be shall be borne by that party at fault.

Any case of obstruction falls into one of two categories generally called type " A " and type " B ", after the subsection of Official Baseball Rule 7. 06, in which each type of obstruction is described.

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.