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

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

* 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 ordinal number can be made into a topological space by endowing it with the order topology ( since, being well-ordered, an ordinal is in particular totally ordered ): in the absence of indication to the contrary, it is always that order topology which is meant when an ordinal is thought of as a topological space.

* Any continuous map of topological spaces determines a sheaf of sets.

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 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 DAG has at least one topological ordering, and algorithms are known for constructing a topological ordering of any DAG in linear time.

* Any uniform space ( hence any metric space, topological vector space, or topological group ) is a Cauchy space ; see Cauchy filter for definitions.

Any topological space X gives rise to a category where the objects are the points of X and the morphisms are the homotopy classes of paths.

Any topological manifold can be given a differential structure locally by using the homeomorphisms in its atlas and the standard differential structure on a linear space.

Any topological space which deformation retracts to a point is contractible.

1 ) Any non-diagonalizable intersection form gives rise to a four-dimensional topological manifold with no differentiable structure ( so cannot be smoothed ).

Any point on the boundary between these two sets is both a left and right topological divisor of zero.

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

Any attempt to reconcile this statement of the central issue in the campaign of 1956 with the nature of the man who could not conceive it as the central issue will at least resolve our confusions about the chaotic and misleading results of the earnestness of both doctors and President in a situation which should never have arisen.

Any free elections that were to be held in Poland would have to produce a government in which Moscow had complete confidence, and all pressure from the West for free voting by anti-Soviet elements in Poland would be met by restrictions on voting by these elements.

Any street meeting, sacred or secular, which he and his colleagues uneasily cover has as its explicit or implicit burden the cruelty and injustice of the white domination.

Any adjustments which are made, Mr. Grenier said earlier this month, will appear on the balance of the tax bill since most of the town's taxpayers take the option of paying quarterly with the balance due next year.

Section 72 says " Any person who takes part in a fight in a public place, or takes part in a fight of such a nature as to alarm the public in any other place to which the public have access, commits a misdemeanour.

Any difference between the hedged positions represents any remaining risk ( such as basis risk ) plus profit ; the belief is that there remains some difference which, even after hedging most risk, represents pure profit.

Any pellets which are too small to be finished granules of couscous and fall through the sieve will be again rolled and sprinkled with dry semolina and rolled into pellets.

# Any experience which is inconsistent with the organization of the structure of the self may be perceived as a threat, and the more of these perceptions there are, the more rigidly the self structure is organized to maintain itself.

Any violations of Ahura Mazda's order arise from druj, which is everything uncreated.

Any configuration of charges or currents has a ' dipole moment ', which describes the dipole whose field is the best approximation, at large distances, to that of the given configuration.

Any convex polyhedron can be distorted into a canonical form, in which a midsphere ( or intersphere ) exists tangent to every edge, such that the average position of these points is the center of the sphere, and this form is unique up to congruences.

Any function itself defines an equivalence relation on according to which if and only if.

Any byte in the entire file can be owned by at most one section, and there can be orphan bytes which are not owned by any section.

Any theory in which these principles apply produces the inequalities.

* push in the back – Any tackle which forces the player forward, into the ground, or both, from behind.

Any movement ( from straight and level flight for example ) results in signals to the computer, which automatically moves control actuators to stabilize the aircraft.

Any greater precision depends more on choice of standard than on more careful measurement: the length of the equator in the World Geodetic System WGS-84 is 40, 075, 016. 6856 m which makes the geographical mile 1855. 3248 m, while the International Astronomical Union standard IAU-2000 takes the equator to be 40, 075, 035. 5351 m making the geographical mile 1855. 3257 m, almost a millimetre longer.

Any player entering or leaving the play must cross the substitution line which is part of the side line and extends 4. 5 meters from the middle line to the team's side.

Under Bogart's Santana Productions, which released through Columbia Pictures, Bogart starred in Knock on Any Door ( 1949 ), Tokyo Joe ( 1949 ), In a Lonely Place ( 1950 ), Sirocco ( 1951 ) and Beat the Devil ( 1954 ).

Any ecstatic states or other unusual phenomena which may occur in the course of Hesychast practice are considered secondary and unimportant, even quite dangerous.

Any thunderstorm which produces hail that reaches the ground is known as a hailstorm.

Any foreigners who came to Paraguay during his rule ( which would have been very difficult ) were not allowed to leave for the rest of their life.

# Any true image of Jesus must be able to represent both his divine nature ( which is impossible because it cannot be seen nor encompassed ) as well his human nature.

Any appeals for which notice is filed after that date will be handled by the Residual Mechanism.