|
In mathematics, a closed manifold is a type of topological space, namely a compact manifold without boundary. In contexts where no boundary is possible, any compact manifold is a closed manifold. Compact manifolds are, in an intuitive sense, "finite". By the basic properties of compactness, a closed manifold is the disjoint union of a finite number of connected closed manifolds. One of the most basic objectives of geometric topology is to understand what the supply of possible closed manifolds is. ==Examples== The simplest example is a circle, which is a compact one-dimensional manifold. Other examples of closed manifolds are the torus and the Klein bottle. As a counterexample, the real line is not a closed manifold because it is not compact. A disk is a compact two-dimensional manifold, but is not a closed manifold because it has a boundary. 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「closed manifold」の詳細全文を読む スポンサード リンク
|