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. The cone of X is denoted by C X {\displaystyle CX} or by cone ⁡ ( X ) {\displaystyle \operatorname {cone} (X)} .

In this lecture, we consider the motion of a 3D rigid body. We shall see that in the general three-dimensional case, the angular velocity of the body can change in magnitude as well as in direction, and, as a consequence, the motion is considerably …

The spacetime diagram that corresponds to it looks like a cone. As we proceed up the cone, we look in each instantaneous space to see how far the light has propagated. Each intersection of the cone with the space will be a circle.

A convex cone is a cone that is also closed under addition, or, equivalently, a subset of a vector space that is closed under linear combinations with positive coefficients. It follows that convex cones are convex sets .

In special and general relativity, a light cone (or "null cone") is the path that a flash of light, emanating from a single event (localized to a single point in space and a single moment in time) and traveling in all directions, would take through spacetime.

2016年6月10日 · A cone in an Euclidean space is a set $K$ consisting of half-lines emanating from some point $0$, the vertex of the cone. The boundary $\partial K$ of $K$ (consisting of half-lines called generators of the cone) is part of a conical surface, and is sometimes also called a …

2025年3月5日 · The space join of a topological space X and a point P, C(X)=X*P. TOPICS Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology Alphabetical Index New in MathWorld

这篇笔记，首先我会对三种常见cone从几何角度出发做一个区分，再谈一下cone与 optimality condition 之间密不可分的联系。 今天的主角cone有三位，分别是： Tangent cone 、 linearized cone 、 feasible direction 。

The net result of these two precessional motions is that precesses \( \omega \) in space about the space-fixed angular momentum vector in a cone called the space cone. For a prolate top, the semi vertical angle of the space cone can be anything from 0 ° to 90 ° ; for an oblate top, however, the semi vertical angle of the space cone cannot ...

Given any topological space X, one may construct the cone space and the sus-pension of X (used in algebraic topology), both as a quotient space of the cylinder X [0;1]: (1)The cone...