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Page "Cofinality" ¶ 5
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Every and cofinal
Every partially ordered set is cofinal in itself.

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 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 a nowhere dense set is nowhere dense, and the union of finitely many nowhere dense sets is nowhere dense.
* 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 partially
** Antichain principle: Every partially ordered set has a maximal antichain.
Most of his films have been at least partially financed by Telefilm Canada, and Cronenberg is a vocal supporter of government-backed film projects, saying " Every country needs system of government Grant ( money ) | grants in order to have a national cinema in the face of Hollywood ".
* Every non-empty set of left ideals of R, partially ordered by inclusion, has a maximal element with respect to set inclusion.
Every relatively atomic partially ordered set with a least element is atomic.
Her recording debut was actually made in 1978 when she sang back-up ( and partially lead ) vocals for The Michael Zager Band's " Life's a Party " and background vocals on Chaka Khan's hit single " I'm Every Woman "— a song she would turn into a larger hit for herself in 1993.

Every and ordered
Every non-empty totally ordered set is directed.
Every subfield of an ordered field is also an ordered field in the inherited order.
Every ordered field contains an ordered subfield that is isomorphic to the rational numbers.
Every ordered field is a formally real field.
Every subfield of an ordered field is also an ordered field ( inheriting the induced ordering ).
Every ordered field can be embedded into the surreal numbers.
Every ordered field is a formally real field, i. e., 0 cannot be written as a sum of nonzero squares.
* Every totally ordered set with the order topology is Tychonoff.
* Every totally ordered set that is a bounded lattice is also a Heyting algebra, where is equal to when, and 1 otherwise.
* Every totally ordered set is a distributive lattice with max as join and min as meet.
Every ordered basis lives in one equivalence class or another.
Every time she entered, song typical of the Brazilian northeast would play, stopping only when ordered by Cirene herself.

Every and set
: Every set has a choice function.
** Well-ordering theorem: Every set can be well-ordered.
* 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 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 >.

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