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Some Related Sentences
Conversely and subset

* 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, a complete
subset of
a metric space is closed
.
Conversely, every Polish space is homeomorphic
to a G < sub > δ </ sub >-
subset of the Hilbert cube
.
Conversely, words
such as banjee
, while well-established
in a subset of gay society
, have never made the transition
to popular use
.

Suppose S is an immersed submanifold of M
. If the inclusion map i: S → M is closed then S is actually an embedded submanifold of M
. Conversely, if S is an embedded submanifold which is also
a closed
subset then the inclusion map is closed
.
Conversely and R
Conversely, if ƒ: C → C is
a function which is differentiable when regarded as
a function on
R < sup > 2 </ sup >, then ƒ is complex differentiable
if and only if the Cauchy – Riemann equations hold
.
Conversely, given central idempotents
a < sub > 1 </ sub >,...,
a < sub > n </ sub >
in R that are pairwise orthogonal
and have sum 1
, then
R is the direct sum of the rings Ra < sub > 1 </ sub >,…, Ra < sub > n </ sub >.
Conversely in rings with unity
, any simple left
R module arises this way
.

**
Conversely, if ƒ: I →
R is absolutely continuous
and thus differentiable almost everywhere
, and satisfies | ƒ ′(
x )| ≤ K
for almost all
x in I
, then ƒ is Lipschitz continuous with Lipschitz constant at most K
.
Conversely, it is possible
to 2-colour
a K < sub > 5 </ sub > without creating
any monochromatic K < sub > 3 </ sub >, showing
that R ( 3
, 3
) > 5
.
Conversely, if R is
a symmetric relation over
a set
X, one can interpret it as describing an undirected graph with the elements of
X as the vertices
and the pairs
in R as the edges
.
Conversely, an exhaustive firing test of the M1918 Chauchat
in. 30-06 was also carried out
in 1994 near Chambersburg
, Pennsylvania
, by
R. Keller
and W
. Garofalo
.
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, given
a Boolean ring
R, we define the join operation by
a ' b =
a + b + ab
, and the meet operation as multiplication
.
Conversely, if this identity holds
in a ring
R for all pairs of elements
a and b of the ring
, then
R is commutative
.
Conversely and defines
Conversely, Psychology
defines bottom-up processing as an approach wherein
there is
a progression from the individual elements
to the whole
.
Conversely, given
a commutative diagram
, it
defines a poset category:
Conversely, a system of n quantities v < sup > i </ sup >
that transform like the coordinates
x < sup > i </ sup > on V
defines a contravariant vector
.

Thus
, b < sub > q </ sub > is
a symmetric bilinear form over K with matrix A
. Conversely, any symmetric bilinear form b
defines a quadratic form
Conversely the building can be recovered from the BN pair
, so
that every BN pair canonically
defines a building
.

where e is the identity
in G
. Conversely, given
a section s one
defines a trivialization Φ by
Conversely, any operator satisfying the above properties
defines a connection on E
and a connection
in this sense is also known as
a covariant derivative on E
.
Conversely, an Ehresmann connection H ⊂ TP
( or v: TP → V
) on P
defines a principal G-connection ω
if and only if it is G-equivariant
in the sense
that.
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, a crossed module with surjective boundary
defines a central extension
.
Conversely, singly even dimensional manifolds have
a skew-symmetric nondegenerate bilinear form on their middle dimension ;
if one
defines a quadratic refinement of this
to a quadratic form
( as on
a framed manifold ), one obtains the Arf invariant as
a mod 2 invariant
.
Conversely and binary
Conversely, in a preadditive category
, every
binary equaliser can be constructed as
a kernel
.
Conversely and function
Conversely, function application is considered
to be left-associative
, so
that is equivalent
to.
Conversely, sociology of law may help comparative law answer questions
, such as: How do regulations
in different legal systems really
function in the respective societies?
Conversely, in functional code
, the output value of
a function depends
only on the arguments
that are input
to the
function, so calling
a function f twice with the same value
for an argument
x will produce the same result f
( x ) both times
.
Conversely, given
a harmonic
function, it is the real part of an analytic
function, ( at least locally ).
Conversely most
( but not all
) of the ASCII " control characters " have some control
function in isolation
, therefore are not escape characters
.
Conversely, given
any harmonic
function in two dimensions
, it is the real part of an analytic
function, at least locally
.
Conversely, those who wish
to function primarily as clinical ED physicians choose the CCFP route of certification
.
Conversely, warming of an affected extremity may indicate
a disruption of the body's normal thermoregulatory vasoconstrictor
function, which may sometimes indicate underlying CRPS
.
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
.
Conversely, any equation can take the canonical form f
( x ) = 0
, so equation solving is the same thing as computing
( or finding
) a root of
a function.

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, by the inverse
function theorem
, there can be at most one value
for σ
that, when applied as an input
to, will result
in a particular value
for C
.
Conversely, culture decline is
a function of the feckless mixture of Aryan
, with lesser ' animalistic ,' blood ...
Conversely, if it is too wet
, mud cakes
in the machinery
and moisture weighs down the material
, making it impossible
for the equipment
to function without picking up large quantities of mud
.
Conversely, a single email address may be an alias
and have
a distribution
function to many mailboxes
.
Conversely, there may be levels of production where marginal cost is higher than average cost
, and average cost is an increasing
function of output
.
Conversely, a function u: E < sub > 1 </ sub > → E < sub > 2 </ sub > defined on
a basis of E < sub > 1 </ sub > can be uniquely extended
to a linear
function.
0.291 seconds.