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 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 decision in allocating capital is likewise: there is an opportunity cost of capital, or a hurdle rate, defined as the expected rate one could get by investing in similar projects on the open market.

Any legal wrestler is open to attack from any direction at any time, including when they are downed, as long as they are within the ring area enclosed by the ring ropes.

Any canal built open to all nations on equal terms.

Eric Raymond extends this principle in support of open source security software, saying, " Any security software design that doesn't assume the enemy possesses the source code is already untrustworthy ; therefore, never trust closed source.

* 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 finite subcover of this cover must be bounded, because all balls in the subcover are contained in the largest open ball within that subcover.

Any real analytic function on some open set on the real line can be extended to a complex analytic function on some open set of the complex plane.

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

* Aranym Atari Running on Any Machine: an open source emulator / virtual machine that can run Atari GEM applications

According to the historian of science Norwood Russell Hanson: There is no bilaterally-symmetrical, nor excentrically-periodic curve used in any branch of astrophysics or observational astronomy which could not be smoothly plotted as the resultant motion of a point turning within a constellation of epicycles, finite in number, revolving around a fixed deferent. Any path — periodic or not, closed or open — can be represented with an infinite number of epicycles.

( 2 ) Any non-profit corporation, civic association, or governmental entity which has buildings and grounds open to the public may request for the appointment of constables to serve as law enforcement officers in order to protect life and property.

* 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 open set is trivially a G < sub > δ </ sub > set

Any competitors desiring their names to be attached to their contributions will please give permission to the Committee to open the envelopes inscribed with their mottoes.

Any open cover of a paracompact space is numerable.

Any future attempt to recover his throne would have to be with the open support of the English king.

Any point x gives rise to a continuous function p < sub > x </ sub > from the one element topological space 1 ( all subsets of which are open ) to the space X by defining p < sub > x </ sub >( 1 ) = x. Conversely, any function from 1 to X clearly determines one point: the element that it " points " to.

Any given open cover of the unit circle will have a refinement consisting of a collection of open arcs.

Any subset of B is also well-ordered.

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

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 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 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 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.