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Page "Alexandrov topology" ¶ 9
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Every and point
Every Halloween, Dabney House conducts the infamous " Millikan pumpkin-drop experiment " from the top of Millikan Library, the highest point on campus.
* 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 ultrafilter on X converges to at least one point.
# 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 point in three-dimensional Euclidean space is determined by three coordinates.
Every gymnast starts at a different point on the vault runway depending on their height and strength.
Every time a stopper stops the raider from going back to his starting point, that stoppers team gets 1 point.
Every point on the Lorenz curve represents a statement like " the bottom 20 % of all households have 10 % of the total income.
Every ferromagnetic substance has its own individual temperature, called the Curie temperature, or Curie point, above which it loses its ferromagnetic properties.
Every patient with a point total of 6 or higher is unequivocally classified as an RA patient, provided he has synovitis in at least one joint and given that there is no other diagnosis better explaining the synovitis.
Historian Barry Adam notes, " Every social movement must choose at some point what to retain and what to reject out of its past.
From a pro-independence supporter's point of view, the movement for Taiwan independence began under Qing rule in the 1680s which led to a well known saying those days, " Every three years an uprising, every five years a rebellion ".
Every number is thought of as a decimal fraction with the initial decimal point omitted, which determines the filing order.
Every non-empty intersection of a 3-sphere with a three-dimensional hyperplane is a 2-sphere ( unless the hyperplane is tangent to the 3-sphere, in which case the intersection is a single point ).
Every point that is expressed in ellipsoidal coordinates can be expressed as an ( Cartesian ) coordinate.
Maxwell Fyfe brought up Raeder's order of 15 October 1939, which read: " Measures which are considered necessary from a military point of view will have to be carried out, even if they are not covered by existing international law ... Every protest from neutral powers will have to be turned down ... The more ruthlessly economic warfare is waged ... the sooner the war will come to an end ".
Every material has a critical angle, at which point light is reflected back internally.
Every point constructible using straightedge and compass may be constructed using compass alone.
( As one later wrote of finally being forced to make an anti-American statement: " I had learned what we all learned over there: Every man has his breaking point.
Every time he throws a point above ten ( or passes ten -- whence the name of the game ), the banker must double the player's stakes and the stakes of all those who have risked their money on the same chance.
Every year at breakup, families moved up into the hills from the point.

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 net on X has a convergent subnet ( see the article on nets for a proof ).
# Every filter on X has a convergent refinement.
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.

Every and has
Every soldier in the army has, somewhere, relatives who are close to starvation.
Every woman has had the experience of saying no when she meant yes, and saying yes when she meant no.
Every detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he is playing with Viennese musicians ), and the gossamer shading throughout.
Every calculation has been made independently by two workers and checked by one of the editors.
Every retiring person has a different situation facing him.
Every family of Riviera Presbyterian Church has been asked to read the Bible and pray together daily during National Christian Family Week and to undertake one project in which all members of the family participate.
Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.
`` Every woman in the block has tried that ''.
: 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.
** 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.
** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.
** Antichain principle: Every partially ordered set has a maximal antichain.
** Every vector space has a basis.
* Every small category has a skeleton.
* 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 field has an algebraic closure.
** Every field extension has a transcendence basis.
** Every Tychonoff space has a Stone – Čech compactification.
* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =
Every unit of length has a corresponding unit of area, namely the area of a square with the given side length.
Every field has an algebraic extension which is algebraically closed ( called its algebraic closure ), but proving this in general requires some form of the axiom of choice.
Every ATM cell has an 8-or 12-bit Virtual Path Identifier ( VPI ) and 16-bit Virtual Channel Identifier ( VCI ) pair defined in its header.

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