Any two regular curves are locally isometric.

Any such stress-energy pseudotensor can be made to vanish locally by a coordinate transformation.

Any affine scheme is separated, therefore any scheme is locally separated.

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 scrub typhus vaccine should give protection to all the strains present locally, in order to give an acceptable level of protection.

** Without the DNS Client service running: Any fallback to the alternative DNS servers happen locally, within each individual process that is making DNS queries.

Any compact Riemann surface of genus greater than 1 ( with its usual metric of constant curvature − 1 ) is a locally symmetric space but not a symmetric space.

* Any compact group is locally compact.

* Any discrete group is locally compact.

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

* Any space carrying the cofinite topology is compact.

Note that for orientable compact surfaces without boundary, the Euler characteristic equals, where is the genus of the surface: Any orientable compact surface without boundary is topologically equivalent to a sphere with some handles attached, and counts the number of handles.

Concerned with the runaway success of the Ford Mustang, Chevrolet executives realized that their compact sporty car, the Corvair, would not be able to generate the sales volume of the Mustang due to its rear-engine design, as well as declining sales, partly due to the bad publicity from Ralph Nader's book, Unsafe at Any Speed.

Any compact orientable surface and any compact surface with non-empty boundary embeds in though any closed non-orientable surface needs.

Any bounded operator L that has finite rank is a compact operator ; indeed, the class of compact operators is a natural generalisation of the class of finite-rank operators in an infinite-dimensional setting.

* Any compact operator is strictly singular, but not vice-versa.

Any compact manifold has isoperimetric dimension 0.

* Any compact symplectic manifold admits a symplectic Lefschetz pencil ( Donaldson 1999 ).

( 2 ) Any sequence of continuous positive definite functions on G converging to 1 uniformly on compact subsets, converges to 1 uniformly on G.

The canonical ring and therefore likewise the Kodaira dimension is a birational invariant: Any birational map between smooth compact complex manifolds induces an isomorphism between the respective canonical rings.

* Any countable union or intersection of Lusin subspaces of a Hausdorff space is Lusin.

Any Hausdorff ( T < sub > 2 </ sub >) space is sober ( the only irreducible subsets being points ), and all

Any connected Lie group can be built up by means of its infinitesimal generators ( a basis for the Lie algebra of the group ); with explicit if not always useful information given in the Baker – Campbell – Hausdorff formula.

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