In functional analysis, a branch of mathematics, a bounding point of a subset of a vector space is a conceptual extension of the boundary of a set.

Let ${\displaystyle A}$ be a subset of a vector space ${\displaystyle X}$. Then ${\displaystyle x\in X}$ is a bounding point for ${\displaystyle A}$ if it is neither an internal point for ${\displaystyle A}$ nor its complement.^[1]