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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 continuous map f: X → Y induces an algebra homomorphism C ( f ): C ( Y ) → C ( X ) by
the rule C ( f )( φ ) = φ o f for
every φ
in C ( Y ).
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 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 function

:
Every set has
a choice
function.
Every such subset has
a smallest element
, so to specify our choice
function we
can simply say that it maps each set to
the least element
of that set
.

**
Every surjective
function has
a right inverse
.

:
Every effectively calculable
function is
a computable
function.
Every effectively calculable
function ( effectively decidable predicate ) is general recursive italics
Every effectively calculable
function ( effectively decidable predicate ) is general recursive
.
Every bijective
function g has an inverse g < sup >− 1 </ sup >, such that gg < sup >− 1 </ sup > = I ;
Every entire
function can be represented as a power series that converges uniformly on compact sets
.
Every holomorphic
function can be separated into its real and imaginary parts
, and each
of these is
a solution
of Laplace's equation on R < sup > 2 </ sup >.
Every holomorphic
function is analytic
.
Every completely multiplicative
function is
a homomorphism
of monoids and is completely determined by its restriction to
the prime numbers
.
Every polynomial P
in x corresponds to
a function, ƒ ( x )
Every primitive recursive
function is
a general recursive
function.
Every time another object or customer enters
the line to wait
, they join
the end
of the line and represent
the “ enqueue ”
function.
Every function is
a method and methods are always called on an object
.
Every type that is
a member
of the type class defines
a function that will extract
the data from
the string representation
of the dumped data
.
Every output
of an encoder
can be described by its own transfer
function, which is closely related to
the generator polynomial
.
Every and space

**
Every vector space has
a basis.

**
Every infinite game
in which is
a Borel subset
of Baire
space is determined
.

**
Every Tychonoff
space has
a Stone – Čech compactification
.

* Theorem
Every reflexive normed
space is
a Banach
space.
Every Hilbert
space X is
a Banach
space because
, by definition
, a Hilbert
space is complete with respect to
the norm associated with its inner product
, where
a norm and an inner product are said to
be associated if for all x ∈ X
.

*
Every topological
space X is
a dense subspace
of a compact
space having at most one point more than X
, by
the Alexandroff one-point compactification
.

*
Every compact metric
space is separable
.
Every subset A
of the vector space is contained within
a smallest convex set ( called
the convex hull
of A ), namely
the intersection
of all convex sets containing A
.
Every compact metric
space is complete
, though complete spaces need not
be compact
.
Every point
in three-dimensional Euclidean
space is determined by three coordinates
.
Every node on
the Freenet network contributes storage
space to hold files
, and bandwidth that it uses to route requests from its peers
.

*
Every Lie group is parallelizable
, and hence an orientable manifold ( there is
a bundle isomorphism between its tangent bundle and
the product
of itself with
the tangent
space at
the identity )
Every vector space has
a basis, and all bases
of a vector space have
the same number
of elements
, called
the dimension
of the vector space.
Every normed
vector space V sits
as a dense subspace inside
a Banach
space ; this Banach
space is essentially uniquely defined by V and is called
the completion
of V
.
0.132 seconds.