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2. Cone (topology) - Wikipedia

   en.wikipedia.org/wiki/Cone_(topology)

   The cone over a closed interval I of the real line is a filled-in triangle (with one of the edges being I), otherwise known as a 2-simplex (see the final example). The cone over a polygon P is a pyramid with base P. The cone over a disk is the solid cone of classical geometry (hence the concept's name). The cone over a circle given by

3. Cone - Wikipedia

   en.wikipedia.org/wiki/Cone

   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 ]

4. Projective cone - Wikipedia

   en.wikipedia.org/wiki/Projective_cone

   Let X be a projective space over some field K, and R, S be disjoint subspaces of X. Let A be an arbitrary subset of S. Then we define RA, the cone with top R and basis A, as follows : When A is empty, RA = A. When A is not empty, RA consists of all those points on a line connecting a point on R and a point on A.

5. Convex cone - Wikipedia

   en.wikipedia.org/wiki/Convex_cone

   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.

6. Tangent cone - Wikipedia

   en.wikipedia.org/wiki/Tangent_cone

   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.

7. Dual cone and polar cone - Wikipedia

   en.wikipedia.org/wiki/Dual_cone_and_polar_cone

   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.