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The points of X that are defined over F < sub >< span > p < sup > n </ sup ></ span ></ sub > are those fixed by F < sup > n </ sup >, where F is the Frobenius automorphism in characteristic p.
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points and X
* Uniform algebra: A Banach algebra that is a subalgebra of C ( X ) with the supremum norm and that contains the constants and separates the points of X ( which must be a compact Hausdorff space ).
* Natural Banach function algebra: A uniform algebra whose all characters are evaluations at points of X.
* Cone ( topology ) of a set X, namely the union of all line segments connecting a fixed point to points of X
An important extension of this idea is to consider the fundamental groupoid ( X, A ) where A is a set of " base points " and a subset of X.
X is a Hausdorff space if any two distinct points of X can be separated by neighborhoods.
X is a preregular space if any two topologically distinguishable points can be separated by neighbourhoods.
A first countable, separable Hausdorff space ( in particular, a separable metric space ) has at most the continuum cardinality c. In such a space, closure is determined by limits of sequences and any sequence has at most one limit, so there is a surjective map from the set of convergent sequences with values in the countable dense subset to the points of X.
In other words, Y is colored in a two-step process: First, for every x in X, the point f ( x ) is colored green ; Second, all the rest of the points in Y, that are not green, are colored blue.
It turns out that the crucial property that a subalgebra must satisfy is that it separates points: a set A of functions defined on X is said to separate points if, for every two different points x and y in X there exists a function p in A with p ( x ) not equal to p ( y ).
Then A is dense in C ( X, R ) if and only if it separates points.
Trailing 10-7 in the fourth quarter of Super Bowl X, the Steelers rallied to score 14 unanswered points, including a 64-yard touchdown reception by Pittsburgh wide receiver Lynn Swann.
Let X be a set ; the elements of X are usually called points, though they can be any mathematical objects.
The fourth axiom has a very important use in the structure of the theory, that of linking together the neighbourhoods of different points of X.
For example, when the last order of play before a pair score 5 points in the final game is A → X → B → Y, the order after change shall be A → Y → B → X if A still has the second serve.
points and are
Now let us imagine a wing of B-52's, on alert near their `` positive control ( or fail-safe ) points '', the spots on the map, many miles from Soviet territory, beyond which they are forbidden to fly without specific orders to proceed to their targets.
For the occasion on which everyone already knows everyone else and the host wishes them to meet one or a few honored newcomers, then the `` open house '' system is advantageous because the honored guests are fixed connective points and the drifting guests make and break connections at the door.
In Figure 2, the points in the network are designated by a letter accompanied by a number.
As Critic Walter Kerr points out: `` Adaptations, so long as they are good, still qualify as creative ''.
The Kansas City and the Topeka KCs are arranging that Juniors who win at their shows will be qualified to win points for Westminster.
Such locks are nearly always used where the switch points `` face '' oncoming traffic.
The lock insures that the points are thrown all the way with no chance that a wheel flange will snag on a partly thrown point.
The fact that there can not be any limit points of the set except in closed intervals follows from the argument used in Lemma 1, namely, that near any tangent point in the C-plane the curves C and Af are analytic, and therefore the difference between them must be a monotone function in some neighborhood on either side of the tangent point.
First, for any value of T for which all values of f{t} are ordinary points the number of values of f{t} must be odd.
The remaining ( incomplete ) components all have an even number of ordinary points at any argument, and are defined only on a proper sub-interval of Aj.
We must now show that on some component of the graph there exist two points for which the corresponding diagonal points in the C-plane are on opposite sides of C.
These are defined by a simple involutorial transformation of the points in which a general line meets a nonsingular quadric surface bearing a curve of symbol Af.
A general line L meets Q in two points, Af and Af, through each of which passes a unique generator of the regulus, Af, whose lines are simple secants of Aj.
Moreover, from the definitive transformation of intercepts on the generators of Af, it is clear that the only points of Q at which a line can meet its image are the points of Aj.
The invariant lines are the lines of the congruence of secants of **zg, since each of these meets Q in two points which are invariant.
Since two curves of symbol Af on Q intersect in Af points, it follows that there are Af lines of Af which are tangent to Aj.
If **ya is the multiple secant of **zg which passes through Af and **yb is the simple secant of **zg which passes through Af, and if Af are the points in which **ya meets **zg, and if Af is the image of Af on the generator **yb, it follows that the image of the line Af is Af.
With respect to this view, two points are worth making.
Less ambitious freeway plans may be more successful -- especially when the roadways and interchanges are raised, allowing for cross access at many points and providing parking areas below the ramp.
The brief notes introducing each work offer salient historical or technical points, and many listeners are probably grateful for being intelligently taken by the hand through an often difficult maze.
The Rockies have many `` Aspencades '', which are organized tours of the aspen areas with frequent stops at vantage points for viewing the golden panoramas.
points and defined
From about 1955 he started to work on sheaf theory and homological algebra, producing the influential " Tôhoku paper " ( Sur quelques points d ' algèbre homologique, published in 1957 ) where he introduced Abelian categories and applied their theory to show that sheaf cohomology can be defined as certain derived functors in this context.
For example, using Cartesian coordinates on the plane, the distance between two points ( x < sub > 1 </ sub >, y < sub > 1 </ sub >) and ( x < sub > 2 </ sub >, y < sub > 2 </ sub >) is defined by the formula
Therefore bandwidth can be defined as the difference between the lower and upper half power points.
A Bézier curve is defined by a set of control points P < sub > 0 </ sub > through P < sub > n </ sub >, where n is called its order ( n
Writing B < sub > P < sub > i </ sub >, P < sub > j </ sub >, P < sub > k </ sub ></ sub >( t ) for the quadratic Bézier curve defined by points P < sub > i </ sub >, P < sub > j </ sub >, and P < sub > k </ sub >, the cubic Bézier curve can be defined as a linear combination of two quadratic Bézier curves:
During the second period, the Protestants present asked for renewed discussion on points already defined and for bishops to be released from their oaths of allegiance to the Pope.
The wall nearest us would be defined by four points: ( in the order x, y, z ).
For example, the file to which the link < tt >/ bin / ls </ tt > points in a typical Unix-like system probably has a defined size that seldom changed.
This notion can also be defined locally, i. e. for small neighborhoods of points.
In Euclidean geometry, the ellipse is usually defined as the bounded case of a conic section, or as the set of points such that the sum of the distances to two fixed points ( the foci ) is constant.
The ellipse can also be defined as the set of points such that the distance from any point in that set to a given point in the plane ( a focus ) is a constant positive fraction less than 1 ( the eccentricity ) of the perpendicular distance of the point in the set to a given line ( called the directrix ).
The ellipse can also be defined as the set of points that are equidistant from one focus and a particular circle, the directrix circle, that is centered on the other focus.
In projective geometry, an ellipse can be defined as the set of all points of intersection between corresponding lines of two pencils of lines which are related by a projective map.
By projective duality, an ellipse can be defined also as the envelope of all lines that connect corresponding points of two lines which are related by a projective map.
In analytic geometry, the ellipse is defined as the set of points of the Cartesian plane that, in non-degenerate cases, satisfy the implicit equation
This means that the value of individual social assets that Bourdieu points to depend on the current " social capital " as defined above.
A 4GL is defined as a language that supports 12 – 20 function points per staff month.
# Plano-polar, in which points in a plane are defined by a distance from a specified point along a ray having a specified direction with respect to a base line or axis ;
# Rectangular, points are defined by distances from two perpendicular axes called and.
The median result is defined to be equivalent to 100 IQ points.
In almost all modern tests, a standard deviation of the results is defined to be equivalent to 15 IQ points.
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