|
In topology, especially algebraic topology, the cone ''CX'' of a topological space ''X'' is the quotient space: : of the product of ''X'' with the unit interval ''I'' = (1 ). Intuitively we make ''X'' into a cylinder and collapse one end of the cylinder to a point. If ''X'' sits inside Euclidean space, the cone on ''X'' is homeomorphic to the union of lines from ''X'' to another point. That is, the topological cone agrees with the geometric cone when defined. However, the topological cone construction is more general. ==Examples== * The cone over a point ''p'' of the real line is the interval x (). * The cone over two points is a "V" shape with endpoints at and . * The cone over an interval ''I'' of the real line is a filled-in triangle, 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 is the curved surface of the solid cone: :: :This in turn is homeomorphic to the closed disc. * In general, the cone over an n-sphere is homeomorphic to the closed (''n''+1)-ball. * The cone over an ''n''-simplex is an (''n''+1)-simplex. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Cone (topology)」の詳細全文を読む スポンサード リンク
|