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Conversely, every Polish space is homeomorphic to a G < sub > δ </ sub >- subset of the Hilbert cube.
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Conversely and every
Conversely, every point on the line can be interpreted as a number in an ordered continuum which includes the real numbers.
Conversely every partition of comes from an equivalence relation in this way, according to which if and only if and belong to the same set of the partition.
Conversely, every formally real field can be equipped with a compatible total order, that will turn it into an ordered field.
Conversely, every preorder is the reachability relationship of a directed graph ( for instance, the graph that has an edge from x to y for every pair ( x, y ) with x ≤ y ).
Conversely, though every president from Washington to John Quincy Adams can be definitely assigned membership in an Anglican or Unitarian body, the significance of these affiliations is often downplayed as unrepresentative of their true beliefs.
Conversely, birds of prey-which show distinct reverse sexual dimorphism — tend to be monogamous for long periods or mate for life ; some species like the Snail kite will choose new mates every year, polygyny is noted in many Harriers and polyandry has been observed in the Harris ' Hawk ( notable for being the only bird of prey to regularly live and hunt in family and social groups ) and the aforementioned Galapagos hawk.
Conversely every positive functional φ gives a corresponding inner product < ƒ, g >< sub > φ </ sub > = φ ( g * ƒ ).
Conversely, every positive semi-definite matrix is the covariance matrix of some multivariate distribution.
We define Thm ( C ) to be the set of all formulas that are valid in C. Conversely, if X is a set of formulas, let Mod ( X ) be the class of all frames which validate every formula from X.
Conversely, if we pick every member of the same population with property and ask " what proportion of these have property?
Conversely, every admissible statistical procedure is either a Bayesian procedure or a limit of Bayesian procedures.
As stated earlier, an adjunction between categories C and D gives rise to a family of universal morphisms, one for each object in C and one for each object in D. Conversely, if there exists a universal morphism to a functor G: C → D from every object of D, then G has a left adjoint.
It is a fact that the ring is a principal ideal ring ; that is, for any ideal I in, there exists an integer n in I such that every element of I is a multiple of n. Conversely, the set of all multiples of an arbitrary integer n is necessarily an ideal, and is usually denoted by ( n ).
This ring is the endomorphism ring of A. Conversely, every ring ( with identity ) is the endomorphism ring of some object in some preadditive category.
Conversely, extra lives are earned by collecting heart points, which are earned by defeating enemies or collecting Hearts, with an extra life earned for every 100 points earned.
Conversely the building can be recovered from the BN pair, so that every BN pair canonically defines a building.
Conversely, the following characterization of derived functors holds: given a family of functors R < sup > i </ sup >: A → B, satisfying the above, i. e. mapping short exact sequences to long exact sequences, such that for every injective object I of A, R < sup > i </ sup >( I )= 0 for every positive i, then these functors are the right derived functors of R < sup > 0 </ sup >.
Conversely and Polish
Conversely, the young Polish girls who were selected for " racially valuable traits " and sent to Germany for Germanization were made to join the League as part of the Germanization.
Conversely Wojciechowski's concept aided the governmental demand to legitimize the Polish acquirements in the West
Conversely and space
Conversely, because space is expanding, and more distant objects are receding ever more quickly, light emitted by us today may never " catch up " to very distant objects.
* The spectrum of any bounded linear operator on a Banach space is a nonempty compact subset of the complex numbers C. Conversely, any compact subset of C arises in this manner, as the spectrum of some bounded linear operator.
Conversely, one might expect that inertial motions, once identified by observing the actual motions of bodies and making allowances for the external forces ( such as electromagnetism or friction ), can be used to define the geometry of space, as well as a time coordinate.
Conversely, in the bleak Orwellian world of " The High Ones "— where the Soviets have won the Third World War and gained control of the whole world — the dissidents still have some hope, precisely because space flight has not been abandoned.
Conversely, a metrizable space is separable if and only if it is second countable, which is the case if and only if it is Lindelöf.
Given a vector space V over a field K, the span of a set S ( not necessarily finite ) is defined to be the intersection W of all subspaces of V which contain S. W is referred to as the subspace spanned by S, or by the vectors in S. Conversely, S is called a spanning set of W.
Conversely, except in dimension 2, if the curvature of a Riemannian manifold has this form for some function K, then the Bianchi identities imply that K is constant and thus that the manifold is ( locally ) a space form.
Equipped with this notion of length, a Riemannian manifold is a metric space, meaning that it has a distance function d ( p, q ) whose value at a pair of points p and q is the distance from p to q. Conversely, the metric tensor itself is the derivative of the distance function ( taken in a suitable manner ).
Conversely, when a record is deleted, later records are moved down so that the free space remains contiguous.
Conversely, if X is projective, then the pullback of under the closed immersion of X into a projective space is very ample.
Conversely, if X is a Hausdorff space and ker f is a closed set, then the coimage of f, if given the quotient space topology, must also be a Hausdorff space.
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.
Conversely, any such one form defines ( via pullback ) a G-equivariant horizontal 1-form on P, and the space of principal G-connections is an affine space for this space of 1-forms.