Prove proposition 3.14 for a finite-dimensional space X. [Hint: Apply exercise 3.182 to the set B -

Question:

Prove proposition 3.14 for a finite-dimensional space X. [Hint: Apply exercise 3.182 to the set B - A. Compactness of A is necessary to ensure that B - A is closed.]
The following exercise shows that compactness of A is essential in proposition 3.14.