Search results
Results from the WOW.Com Content Network
Cone of a circle. The original space X is in blue, and the collapsed end point v is in green.. In topology, especially algebraic topology, the cone of a topological space is intuitively obtained by stretching X into a cylinder and then collapsing one of its end faces to a point.
According to the above definition, if C is a convex cone, then C ∪ {0} is a convex cone, too. A convex cone is said to be pointed if 0 is in C, and blunt if 0 is not in C. [2] [21] Blunt cones can be excluded from the definition of convex cone by substituting "non-negative" for "positive" in the condition of α, β.
The definition of a cone may be extended to higher dimensions; see convex cone. In this case, one says that a convex set C in the real vector space R n {\displaystyle \mathbb {R} ^{n}} is a cone (with apex at the origin) if for every vector x in C and every nonnegative real number a , the vector ax is in C . [ 2 ]
If the cone C=Spec X R is the total space of a vector bundle E, then O(-1) is the tautological line bundle on the projective bundle P(E). Remark : When the (local) generators of R have degree other than one, the construction of O (1) still goes through but with a weighted projective space in place of a projective space; so the resulting O (1 ...
A cone C in a vector space X is said to be self-dual if X can be equipped with an inner product ⋅,⋅ such that the internal dual cone relative to this inner product is equal to C. [3] Those authors who define the dual cone as the internal dual cone in a real Hilbert space usually say that a cone is self-dual if it is equal to its internal dual.
The cone graphic shows the areas that will potentially be affected by Hurricane Ian. What does a ‘cone of uncertainty’ mean? What to know about a Hurricane Ian descriptor
Its defining ideal is the principal ideal of k[x] generated by the initial term of f, namely y 2 − x 2 = 0. The definition of the tangent cone can be extended to abstract algebraic varieties, and even to general Noetherian schemes. Let X be an algebraic variety, x a point of X, and (O X,x, m) be the local ring of X at x.
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!