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* 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.
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Any and topological
* Any finite topological space, including the empty set, is compact.
Any topological space which is itself finite or countably infinite is separable, for the whole space is a countable dense subset of itself.
* Any topological space which is the union of a countable number of separable subspaces is separable.
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 and space
* 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 and can
He merely said, `` Any good decorator these days can make you a tasteful home ''.
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 reputable French interne can supply you with a dozen similar instances, and I'll presently recount a case out of my own personal experience, but, for the moment, let's resume our catalogue.
Any needy family living in San Francisco can obtain toys by writing to Christmas Toys, 676 Howard street, San Francisco 5, and listing the parent's name and address and the age and sex of each child in the family between the ages of 1 and 12.
Any breach of these laws is a criminal offence and can lead to fine of up to £ 5, 000 or six months in prison.
Any use of antibiotics can increase selective pressure in a population of bacteria to allow the resistant bacteria to thrive and the susceptible bacteria to die off.
* Any ring A can be considered as a Z-algebra in a unique way.
Any of these body styles can optionally incorporate a " cutaway ".
Any Latin-American country can join the 1980 Montevideo Treaty.
Any given bookmaker will weight their odds so that no one customer can cover all outcomes at a profit against their books.
Any node in the data structure can be reached by starting at root node and repeatedly following references to either the left or right child.
Any Banach algebra ( whether it has an identity element or not ) can be embedded isometrically into a unital Banach algebra so as to form a closed ideal of.
Any of these ways can be criticized for ...
Any Sangiovese-based wine made according to the Chianti guidelines from these vineyards can be labelled and marked under the basic Chianti DOCG should the producer wish to use the designation.
Any units of angular measure can be used for declination, but it is customarily measured in the degrees ( ° ), minutes ( ' ), and seconds ( " ) of sexagesimal measure, with 90 ° equivalent to circle.
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 person who uses the Spanish title of " Doctor " ( or " Dr .") without being included in this Government database can be prosecuted for fraud.
Any player on the kicking team behind the kicker, and including the kicker, can recover the kick.
Any sound that can be sampled can be used.
Any ellipse can be obtained by rotation and translation of a canonical ellipse with the proper semi-diameters.
# Any real number can be added to both sides.
# Any real number can be subtracted from both sides.
# Any real number can be multiplied to both sides.
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