[permalink] [id link]
* Every projective set of reals -- and therefore every analytic set and every Borel set of reals -- is an element of L ( R ).
from
Wikipedia
Some Related Sentences
Every and projective
* Every holomorphic vector bundle on a projective variety is induced by a unique algebraic vector bundle.
Every minimal projective ruled surface other than the projective plane is the projective bundle of a 2-dimensional vector bundle over some curve.
Every rational variety, including the projective spaces, is rationally connected, but the converse is false.
Every compact, connected 2-manifold ( or surface ) is homeomorphic to the sphere, a connected sum of tori, or a connected sum of projective planes.
Every and set
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 continuous functor on a small-complete category which satisfies the appropriate solution set condition has a left-adjoint ( the Freyd adjoint functor theorem ).
* 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 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 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 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 >.
Every and reals
* Every real Banach algebra which is a division algebra is isomorphic to the reals, the complexes, or the quaternions.
* Every unital real Banach algebra with no zero divisors, and in which every principal ideal is closed, is isomorphic to the reals, the complexes, or the quaternions.
* Every set of reals in L ( R ) is Lebesgue measurable ( in fact, universally measurable ) and has the property of Baire and the perfect set property.
Every and therefore
* Every locally compact regular space is completely regular, and therefore every locally compact Hausdorff space is Tychonoff.
Every system is unique to the business drivers it supports, therefore the quality attributes of each system such as fault-tolerance, backward compatibility, extensibility, reliability, maintainability, availability, security, usability, and such other – ilities will vary with each implementation.
Every command of the Bible is the directive of God himself and therefore demands willing observance.
Every case in which a court discovers a violation of the Charter would therefore require a section 1 analysis to determine if the law can still be upheld.
Every subset of the Hilbert cube inherits from the Hilbert cube the properties of being both metrizable ( and therefore T4 ) and second countable.
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 government, therefore, found him an useful servant ; and there was nothing in his opinions or in his character which could prevent him from serving any government.
Every one present has the sad experience, that we are powerless in an isolated condition, while the capitalists are united ; therefore it is the duty of every Cigar Maker to join the organization.
Every member of the rebellion wore a yellow turban as the symbol — and therefore the rebellion became known for it.
Every feature on every manufactured part is subject to variation, therefore, the limits of allowable variation must be specified.
Hearst's account in Every Secret Thing states that she and Yoshimura opposed the action and were therefore assigned to " switch cars " far from the scene.
Every polytype can have monoclinic ( M ) or hexagonal ( H ) symmetry, and therefore some sources label them, for example, not as 6C, but 6H or 6M depending on the symmetry.
Every grammar in Kuroda normal form is monotonic, and therefore, generates a context-sensitive language.
One of the earliest formations of the Kalām argument comes from Al-Ghazali, who wrote, " Every being which begins has a cause for its beginning ; now the world is a being which begins ; therefore, it possesses a cause for its beginning.
0.948 seconds.