在点集拓扑学与欧几里得空间中，凸集（convex set）是一个点集合，其中每两点之间的直线点都落在该点集合中。

• 区间是实数的凸集。
• 依据定义，中空的圆形称为圆（circle），它不是凸集；实心的圆形称为圆盘（disk），它是凸集。
• 凸多边形是欧几理得平面上的凸集，它们的每只角都小于180度。
• 单纯形是凸集，对於单纯形的顶点集合来说，单纯形是它们的最小凸集，所以单纯形也是一个凸包。
• 定宽曲线是凸集。

In Euclidean space, a convex set is the region such that, for every pair of points within the region, every point on the straight line segment that joins the pair of points is also within the region. For example, a solid cube is a convex set, but anything that is hollow or has a dent in it, for example, a crescent shape, is not convex. A convex curve forms the boundary of a convex set.