Every open ball in \(\mathbb{R}^n\) is homeomorphic to \(\mathbb{R}^n\). [1, Example 2.25]

Remarks
  • This shows that boundedness is not a topological property.

References Link to heading

  1. J. Lee, Introduction to Topological Manifolds. New York, NY: Springer New York, 2011. doi:10.1007/978-1-4419-7940-7