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Page "Euclidean space" ¶ 0
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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 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 three-dimensional
Every improper rotation of three-dimensional Euclidean space is rotation followed by a reflection in a plane through the origin.

Every and Euclidean
Every rational number / has two closely related expressions as a finite continued fraction, whose coefficients can be determined by applying the Euclidean algorithm to.
Every circle in Euclidean space is a great circle of exactly one sphere.
* Every triangle group T is a discrete subgroup of the isometry group of the sphere ( when T is finite ), the Euclidean plane ( when T has a Z + Z subgroup of finite index ), or the hyperbolic plane.
Every tame knot in three dimensional Euclidean space has a ' fundamental quandle '.
Every dilation of a Euclidean space that is not a congruence has a unique fixed point that is called the center of dilation.
Every plane B that is completely orthogonalTwo flat subspaces S < sub > 1 </ sub > and S < sub > 2 </ sub > of dimensions M and N of a Euclidean space S of at least M + N dimensions are called completely orthogonal if every line in S1 is orthogonal to every line in S2.

Every and space
** Every vector space has a basis.
** Every infinite game in which is a Borel subset of Baire space is determined.
** Every Tychonoff space has a Stone – Čech compactification.
* Theorem Every reflexive normed space is a Banach space.
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 compact metric space is separable.
* 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.
* Pseudocompact: Every real-valued continuous function on the space is bounded.
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 compact metric space is complete, though complete spaces need not be compact.
Every node on the Freenet network contributes storage space to hold files, and bandwidth that it uses to route requests from its peers.
Every space filling curve hits some points multiple times, and does not have a continuous inverse.
* Every Lie group is parallelizable, and hence an orientable manifold ( there is a bundle isomorphism between its tangent bundle and the product of itself with the tangent space at the identity )
Every vector space has a basis, and all bases of a vector space have the same number of elements, called the dimension of the vector space.
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.

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