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 subspace of a real or complex vector space is a balanced set.

Any point p in the subspace can be given coordinates such that

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

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

Any differential area with normal vector of a given internal surface area, bounding a portion of the body, experiences a contact force arising from the contact between both portions of the body on each side of, and it is given by

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

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

# Any tangent vector at the identity of a Lie group can be extended to a left invariant vector field by left translating the tangent vector to other points of the manifold.

Any point on a ray starting from point with direction ( here is a unit vector ) can be written as

Any force directed parallel to the particle's position vector does not produce a torque.

Any particular vector file format supports only some kinds of primitive objects.

Any non-singular curve on a smooth surface will have its tangent vector T lying in the tangent plane of the surface orthogonal

Any vector that rotates around an axis with an angular speed vector ( as defined before ) satisfies:

Any linear combination of the column vectors of a matrix A can be written as the product of A with a column vector:

Any element in the direct sum of two vector spaces of matrices can be represented as a direct sum of two matrices.

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

Any rotation in three-dimensions can be represented as an axis vector and an angle of rotation.

Any tangent vector at a point of the parametric surface M can be written in the form

Any covector field α has components in the basis of vector fields f. These are determined by

Any kind of animal that often visits or encounters flowers is likely to be a pollen vector to some extent.

# Any mental state can be described as an ( N )- dimensional vector of numeric activation values over neural units in a network.

Any vector bundle V over a manifold may be realized as the pullback of a universal bundle over the classifying space, and the Chern classes of V can therefore be defined as the pullback of the Chern classes of the universal bundle ; these universal Chern classes in turn can be explicitly written down in terms of Schubert cycles.

Any non-zero vector v divides the Euclidean space into two half-spaces bounding the hyperplane v < sup >∧</ sup > orthogonal to v, namely v < sup >+</ sup > and v < sup >−</ sup >.

Any non-zero vector of an irreducible representation is cyclic.

Any smooth function on a symplectic manifold gives rise, by definition, to a Hamiltonian vector field and the set of all such form a subalgebra of the Lie Algebra of symplectic vector fields.

* 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 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 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.