Definition:Closed Upper Half-Space/Boundary

Definition

Let $\H^n$ be the closed n-dimensional upper half-space.

The boundary of $\H^n$, denoted $\partial \H^n$, is a subset of $\H^n$ defined as:

$\partial \H^n := \set { \tuple {x_1, \cdots, x_n} \in \R^n : x_n = 0 }$

Sources

• 2013: John M. Lee: Introduction to Smooth Manifolds (2nd ed.): Chapter $1$: Smooth Manifolds: $\S$ Manifolds with Boundary