Topology MOC

Ball space

The 𝑛-ball 𝔹𝑛 is usually defined as the closed unit-ball in 𝑛-dimensional Real coördinate space ℝ𝑛, i.e.

𝔹𝑛={𝑣∈ℝ𝑛:‖𝑣‖≤1}⊆ℝ𝑛

along with the subspace metric and subspace topology. Its boundary is the (𝑛 −1)-Sphere space.

Properties

• The 𝑛-ball is a Compact space.
• Brouwer’s fixed point theorem
• Retraction theorem

---

tidy | en | SemBr