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Conversely and suppose
Conversely, suppose that M is a simple R-module.
Conversely, suppose we are given ( U, V, W ) satisfying
Conversely, suppose no improvement can be made.
Conversely, suppose the estimate holds.
: Conversely, suppose that φ is a smooth real-valued function on M in a neighborhood of p. Since every smooth function has a local coordinate expression, we may express φ as a function in the coordinates.

Conversely and is
Conversely, if he gives a heavy rating to his own reading, and finds more accurate facts in it than in the others, a point is chalked up for the intrinsic, objective meaningfulness of this type of mediumistic material.
Conversely, a current of one ampere is one coulomb of charge going past a given point per second:
Conversely, an adiabatic process that is irreversible and extracts no work is in an isenthalpic process, such as viscous drag, progressing towards a nonnegative change in entropy.
Conversely, British English favours fitted as the past tense of fit generally, whereas the preference of American English is more complex: AmEng prefers fitted for the metaphorical sense of having made an object " fit " ( i. e., suited ) for a purpose ; in spatial transitive contexts, AmEng uses fitted for the sense of having made an object conform to an unchanged object that it surrounds ( e. g., " fitted X around Y ") but fit for the sense of having made an object conform to an unchanged object that surrounds it ( e. g., " fit X into Y "); and for the spatial senses ( both intransitive and transitive ) of having been matching with respect to contour, with no alteration of either object implied, AmEng prefers fit (" The clothes fit.
Conversely, any algebra whose associator is alternating is clearly alternative.
Conversely, any algebra for which this is true is clearly alternative.
Conversely the use of true brass seems to have declined in Western Europe during this period in favour of gunmetals and other mixed alloys but by the end of the first Millennium AD brass artefacts are found in Scandinavian graves in Scotland, brass was being used in the manufacture of coins in Northumbria and there is archaeological and historical evidence for the production of brass in Germany and The Low Countries areas rich in calamine ore which would remain important centres of brass making throughout the medieval period, especially Dinant – brass objects are still collectively known as dinanterie in French.
Conversely, if a Boolean ring A is given, we can turn it into a Boolean algebra by defining x ∨ y := x + y + ( x · y ) and x ∧ y := x · y.
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.
Conversely, modern biological sciences ( including even concepts such as molecular ecology ) are intimately entwined and dependent on the methods developed through biotechnology and what is commonly thought of as the life sciences industry.
Conversely it may generate too many points in areas where the curve is close to linear.
Conversely, if the second theory is correct, then the Athenians were merely reacting to the Persians attacking them.
Conversely, every Bayesian procedure is admissible.
Conversely the equilibrium position is said to be " far to the left " if hardly any product is formed from the reactants.
Conversely, the islands do not receive the upwellings ( cold streams ) that affect the West African coast, so the air temperature is cooler than in Senegal, but the sea is actually warmer, because the orographic relief of some islands, as Sao Miguel with steep mountains, cover it with rich woods and luxuriant vegetation where the dense moisture condense and soak the plants, rocks, soil, logs, moss etc.
Conversely in francophone Canada, one hundredth of a Canadian dollar is informally called a sou ( penny ), though cent is official in both English and French.
Conversely, an absence of secure cycle-parking is a recurring complaint by cyclists from cities with low modal share of cycling.
* 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 and space
Conversely, a complete subset of a metric space is closed.
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, active directed panspermia has been proposed to secure and expand life in space.
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, if W is subspace of V, then W is itself a vector space under the operations induced by
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, every Polish space is homeomorphic to a G < sub > δ </ sub >- subset of the Hilbert cube.
Conversely, any vector space,, is an affine space over itself.
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.
Conversely a compact metric space is second-countable.
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.

Conversely and Af
Conversely, let G be any polynomial such that Af.

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