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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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## Some Related Sentences

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

**.**

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