Provide an Appropriate Response $z > 0$ And Radius $\mathrm { r }$

Multiple Choice

Provide an appropriate response.
-Which of the following space regions is (are) closed?
i. The hemispherical region centered at the origin with $z > 0$ and radius $\mathrm { r }$ bounded by $0 \leq \mathrm { r } \leq \mathrm { r } _ { \mathrm { O } }$
ii. The $x y$ -plane
iii. The half-space $x > 0$
iv. Space itself

A) ii only
B) ii, iii, and iv
C) ii and iv
D) iv only