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Some Related Sentences
Every and continuous

*
Every continuous functor on a small-complete category which satisfies
the appropriate solution set condition has a left-adjoint
( the Freyd adjoint functor theorem
).
Every character is automatically
continuous from A to
C, since
the kernel of a character is a maximal ideal, which is closed.

*
Every continuous map from a compact space to a Hausdorff space is closed and proper
( i. e.,
the pre-image of a compact set is compact.

* Pseudocompact
: Every real-valued
continuous function on
the space is bounded.
Every contraction mapping is Lipschitz
continuous and hence uniformly
continuous ( for a Lipschitz
continuous function,
the constant k is no longer necessarily less than 1
).
Every space filling curve hits some points multiple times, and does not have a
continuous inverse.

*
Every separable metric space is isometric to a subset of
C (),
the separable Banach space of
continuous functions
→ R, with
the supremum norm.
Every uniformly
continuous function between metric spaces is
continuous.
Every continuous function on a compact set is uniformly
continuous.
Every topological group can be viewed as a uniform space
in two ways ;
the left uniformity turns all left multiplications into uniformly
continuous maps while
the right uniformity turns all right multiplications into uniformly
continuous maps.
Every continuous function
in the function space can be represented as a linear combination of basis functions, just as
every vector
in a vector space can be represented as a linear combination of basis vectors.

*
Every Lipschitz
continuous map is uniformly
continuous, and hence a fortiori
continuous.
Every embedding is injective and
continuous.
Every map that is injective,
continuous and either open or closed is
an embedding ; however there are also embeddings which are neither open nor closed.

*
Every compact Hausdorff space of weight at most
( see Aleph number
) is
the continuous image of
( this does not need
the continuum hypothesis, but is less interesting
in its absence
).
Every place south of
the Antarctic Circle experiences a period of twenty-four hours '
continuous daylight at least once per year, and a period of twenty-four hours '
continuous night time at least once per year.
Every and map
Every vector v
in determines a linear
map from R to taking 1 to v, which can be thought of as a Lie
algebra homomorphism.
Every smooth
( or differentiable
) map φ: M
→ N between smooth
( or differentiable
) manifolds
induces natural linear maps between
the corresponding tangent spaces
:
Every distinct
map projection distorts
in a distinct way.
Every inner automorphism is indeed
an automorphism of
the group G, i. e. it is a bijective
map from G to G and it is a
homomorphism ; meaning
( xy )< sup > a </ sup >

*
Every constant
map is a plot.
Every regular
map of varieties is
continuous in the Zariski topology.
Every real m-by-n matrix yields a linear
map from R < sup > n </ sup > to R < sup > m </ sup >.
Every algebraic curve
C of genus g ≥ 1 is associated with
an abelian variety J of dimension g,
by means of
an analytic
map of
C into J.
Every local homeomorphism is a
continuous and open
map.
Every covering
map is a semicovering, but semicoverings satisfy
the " 2 out of 3 "
rule: given a composition of maps of spaces, if two of
the maps are semicoverings, then so also is
the third.

*
Every bundle of Lie algebras over a smooth manifold defines a Lie algebroid where
the Lie bracket is defined pointwise and
the anchor
map is equal to zero.
Every Möbius transformation is a bijective conformal
map of
the Riemann sphere to itself.

* The embedding theorem
for Stein manifolds states
the following
: Every Stein manifold of complex dimension can be embedded into
by a biholomorphic proper
map.
Every issue of our periodical will therefore include one or more
map supplements, and their design will guarantee a
continuous and easily accessible supplement
in easy-to-manage form with special regard
for those who own Stielers Hand-Atlas, Berghaus ’ s Physical Atlas, and other
map publications of
the ( Perthes
) Institute.
Every map consists of numerous textured polygons carefully positioned
in relation to one another.
Every summer,
the town prepares
for the one-week summer festival, " Finnsnes i Fest ", aiming to put Finnsnes on
the map.

*
Every map can be replaced
by a cofibration via
the mapping cylinder construction

*
Every local diffeomorphism is also a local homeomorphism and therefore
an open
map.
Every element x of G gives rise to a tensor-preserving self-conjugate natural transformation via multiplication
by x on each representation, and hence one has a
map.
Every map has these two bases, but each
map has a different pattern of fixed terrain features.
Every and f
Every homomorphism f: G
→ H of Lie groups
induces a
homomorphism between
the corresponding Lie algebras and.
Every locally constant function from
the real numbers R to R is constant
by the connectedness of R. But
the function
f from
the rationals Q to R, defined
by f ( x
) = 0
for x < π, and
f ( x
) = 1
for x > π, is locally constant
( here we use
the fact that π is irrational and that therefore
the two sets

*
Every continuous function
f: → R is bounded.
Every empty function is constant, vacuously, since there are no x and y
in A
for which
f ( x
) and
f ( y
) are different when A is
the empty set.

Theorem
Every self-adjoint
f in A * can be written as
f
Every order-preserving self-map
f of a cpo
( P, ⊥) has a least fixpoint.
Every bounded positive-definite measure μ on G satisfies μ
( 1
) ≥ 0. improved this criterion
by showing that it is sufficient to ask that,
for every continuous positive-definite compactly supported function
f on G,
the function Δ < sup >– ½ </ sup >
f has non-negative integral with respect to Haar measure, where Δ denotes
the modular function.
Every morphism
f: G
→ H
in Grp has a category-theoretic kernel
( given
by the ordinary kernel of
algebra ker
f =
Every isogeny
f: A
→ B is automatically a group
homomorphism between
the groups of k-valued points of A and B,
for any field k over which
f is defined.
Every solution of
the second half g of
the equation defines a unique direction
for x via
the first half
f of
the equations, while
the direction
for y is arbitrary.
Every deterministic complexity class
( DSPACE
( f ( n )), DTIME
( f ( n ))
for all
f ( n )) is closed under complement, because one can simply add a last step to
the algorithm which reverses
the answer.

*
Every point x of
X is isolated
in its fiber
f < sup >− 1 </ sup >(
f ( x )).
0.467 seconds.