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Some Related Sentences
Every and subset
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.

** Zorn's lemma:
Every non-empty partially ordered
set in which every chain ( i
. e
. totally ordered
subset ) has an upper bound contains at least one maximal element
.

The restricted principle "
Every partially ordered
set has
a maximal totally ordered
subset "
is also equivalent to AC over ZF
.

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

#
Every infinite
subset of X has
a complete accumulation point
.

#
Every infinite
subset of A has at least one limit point in A
.

* Limit point compact:
Every infinite
subset has an accumulation point
.
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 cofinal
subset of a partially ordered
set must contain all maximal elements
of that
set.

*
Every separable metric space
is homeomorphic to
a subset of the Hilbert cube
.

*
Every separable metric space
is isometric to
a subset of the ( non-separable ) Banach space l < sup >∞</ sup >
of all bounded real sequences with
the supremum norm ; this
is known as
the Fréchet embedding
.

*
Every separable metric space
is isometric to
a subset of C (),
the separable Banach space
of continuous functions → R
, with
the supremum norm
.

*
Every separable metric space
is isometric to
a subset of the
Every element s
, except
a possible greatest element
, has
a unique successor ( next element ), namely
the least element
of the subset of all elements greater than s
. Every subset which has an upper bound has
a least upper bound
.

*
Every subset of Baire space or Cantor space
is an open
set in
the usual topology on
the space
.

*
Every arithmetical
subset of Cantor space
of < sup >( or?
Every subset of the Hilbert cube inherits from
the Hilbert cube
the properties
of being both metrizable (
and therefore T4 )
and second countable
.

It
is more interesting that
the converse also holds:
Every second countable T4 space
is homeomorphic to
a subset of the Hilbert cube
.

*
Every totally disconnected compact metric space
is homeomorphic to
a subset of a countable product
of discrete spaces
.

*
Every irreducible closed
subset of P < sup > n </ sup >( k )
of codimension one
is a hypersurface ; i
. e.,
the zero
set of some homogeneous polynomial
.

*
Every finite or cofinite
subset of the natural numbers
is computable
.
Every and nowhere

*
Every closed
nowhere dense set is the boundary
of an open
set.

" Or
, as Rainer Maria Rilke puts it
, "
Every artist
is born in an alien country ; he has
a homeland
nowhere but within his own borders
.
Every and dense
Every morning early
, in
the summer
, we searched
the trunks
of the trees as high as we could reach for
the locust shells
, carefully detached their hooked claws from
the bark where they hung
, and stabled them
, a weird faery herd
, in an angle between
the high roots
of the tulip tree
, where no grass grew in
the dense shade
.

*
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 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
.
Every evening they fly
, often in groups
and sometimes over long distances
, to reach safe roosting sites such as
dense trees or shrubs that impede predator movement
, or
, at higher latitudes
, dense conifers that afford good wind protection
.

*
Every intersection
of countably
many dense open
sets is dense.

*
Every non-empty Baire space
is of second category in itself
, and every intersection
of countably
many dense open subsets
of X
is non-empty
, but
the converse
of neither
of these
is true
, as
is shown by
the topological disjoint sum
of the rationals
and the unit interval 1
.
Every sequence
of A
, B
, and C without immediate repetition
of the same one
is possible
and gives an equally
dense packing for spheres
of a given radius
.
Every autumn
, the dried needles
of this tree forms
a dense carpet on
the forest floor
, which
the locals gather in large bundles to serve as bedding for their cattle
, for
the year round
.
Every and set

:
Every set has
a choice function
.

** Well-ordering theorem:
Every set can be well-ordered
.

** Antichain principle:
Every partially ordered
set has
a maximal antichain
.

*
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 non-empty
set A contains an element B which
is disjoint from A
.

*
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
.
Every corporation
, whether financial or
union, as well as every division
of the administration
, were
set up as branches
of the party
, the CEOs
, Union leaders
, and division directors being sworn-in as section presidents
of the party
.
Every DNS zone must be assigned
a set of authoritative name servers that are installed in NS records in
the parent zone
, and should be installed ( to be authoritative records ) as self-referential NS records on
the authoritative name servers
.

Group actions / representations:
Every group G can be considered as
a category with
a single object whose morphisms are
the elements
of G
. A functor from G to Set
is then nothing but
a group action
of G on
a particular
set, i
. e
. a G-set
.

# " Personality " Argument: this argument
is based on
a quote from Hegel: "
Every man has
the right to turn his will upon
a thing or make
the thing an object
of his will
, that
is to say
, to
set aside
the mere thing
and recreate it as his own ".
Every atom across this plane has an individual
set of emission cones .</ p > < p > Drawing
the billions
of overlapping cones
is impossible
, so this
is a simplified diagram showing
the extents
of all
the emission cones combined
.

*
Every singleton
set
Every processor or processor family has its own machine code instruction
set.
Every set is a class
, no matter which foundation
is chosen
.
Every non-empty totally ordered
set is directed
.

*
Every preorder can be given
a topology
, the Alexandrov topology ;
and indeed
, every preorder on
a set is in one-to-one correspondence with an Alexandrov topology on that
set.
Every binary relation R on
a set S can be extended to
a preorder on S by taking
the transitive closure
and reflexive closure
, R < sup >+=</ sup >.
1.193 seconds.