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Every set X with the cocountable topology is Lindelöf, since every nonempty open set omits only countably many points of X.
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Every and set
: 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.
** Well-ordering theorem: Every set can be well-ordered.
** 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.
** 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 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 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 >.
Every and X
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 net on X has a convergent subnet ( see the article on nets for a proof ).
# Every filter on X has a convergent refinement.
# Every ultrafilter on X converges to at least one point.
# Every infinite subset of X has a complete accumulation point.
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 linear combination of its components Y = a < sub > 1 </ sub > X < sub > 1 </ sub > + … + a < sub > k </ sub > X < sub > k </ sub > is normally distributed.
Every significant section of roadway maintained by the state is assigned a number, officially State Highway Route X but commonly called Route X by the NJDOT and the general public.
Every variable X < sub > i </ sub > in the sequence is associated with a Bernoulli trial or experiment.
* Every X is a Y.
Every Gauss – Markov process X ( t ) possesses the three following properties:
Every time someone gave an answer that was not on the board, the family lose a life, accompanied by a large " X " on the board with the infamous " uh-uhh " sound.
Every sigma-ideal on X can be recovered in this way by placing a suitable measure on X, although the measure may be rather pathological.
* 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 cover is a local homeomorphism — that is, for every, there exists a neighborhood of c and a neighborhood of such that the restriction of p to U yields a homeomorphism from U to V. This implies that C and X share all local properties.
Every universal cover p: D → X is regular, with deck transformation group being isomorphic to the fundamental group.
Every cumulant is just μ times the corresponding cumulant of the constant random variable X = 1.
Every closed point of Hilb ( X ) corresponds to a closed subscheme of a fixed scheme X, and every closed subscheme is represented by such a point.
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