数学上，闭流形是指无边界的紧致流形。如讨论背景中的流形不可能有边界，那么紧致流形都是闭流形。留意闭流形中的「闭」是指封闭，不是拓扑学概念的闭集。

闭流形从直观意义来说是「有限」的。按照紧致性的基本性质，一个闭流形是有限个连通闭流形的不交并。几何拓扑学的根本目标之一，是了解可能出现的闭流形。

闭流形的最简单例子是圆形，这是一维的闭流形。二维闭流形（闭曲面）的简单例子有环面和克莱因瓶。一个非例子是直线，虽然是无边界流形，但不是紧致。另一个非例子是闭圆盘，虽然是紧致流形，但有边界。

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.