0

My teacher said (without explaining why) that because $R^{n}$ is finite dimensional then set of all linear functions (Dual space) is equal to the set of all continuous linear functions. Can someone explaining why this true?

Thank you.

gbd
  • 1,963
  • 2
    This can be done by picking a basis in ${\bf R}^{n}$ and examining a particular basis for the dual space and showing that this is indeed a basis. The particular basis is the dual basis {https://en.wikipedia.org/wiki/Dual_basis} – avs May 17 '17 at 18:22
  • 2
    Every linear map of finite dimensional vector spaces is continous https://math.stackexchange.com/questions/112985/every-linear-mapping-on-a-finite-dimensional-space-is-continuous – JJR May 17 '17 at 18:32

0 Answers0