Determine if the given subset of $R ^ { 3 }$ is open, closed, both open and closed, or neither open nor closed. All points $( x , y , z )$ so that $x \geq 1$ , $y 0$ A) Open B) Closed C) Both open and closed D) Neither open nor closed

Question

Determine if the given subset of $R ^ { 3 }$ is open, closed, both open and closed, or neither open nor closed. All points $( x , y , z )$ so that $x \geq 1$ , $y < 0$ and $z > 0$
A) Open
B) Closed
C) Both open and closed
D) Neither open nor closed

Quizplus · Accepted Answer

The subset is neither open nor closed. It is not open because it includes points on the boundary $x = 1$, but does not include an open neighborhood around those points due to the strict inequalities for $y$ and $z$. It is not closed because it does not contain all its limit points; for example, points arbitrarily close to $y = 0$ or $z = 0$ from the negative or positive direction, respectively, are not included in the set.

Determine If the Given Subset Of R3R ^ { 3 }R3

Determine If the Given Subset Of $R ^ { 3 }$