Topological disc ($D^n$)

An $n$-dimensional topological disc is a space homeomorphic to a Euclidean ball in ${\mathbb{R}}^n$, with its open or closed convention specified. A closed disc is homeomorphic to $D^n=\{x\in {\mathbb{R}}^n:|x|\le 1\}$. The planar disk is the Euclidean two-dimensional instance, rather than the whole abstract topological class.

A closed $n$-disc is a space homeomorphic to $D^n=\{x\in {\mathbb{R}}^n:|x|\le 1\}$; its boundary is the sphere $S^{n-1}$.