The SlugMath Wiki is under heavy development!

# Struct/Half open square

Title: Half-open square

A half-open square in $\RR^2$ is given by: $$A = \{ (x,y) \in \RR^2 \mbox{ such that } -1 \leq x \leq 1, -1 < y < 1 \}.$$

When $\RR^2$ is viewed as a metric space with the usual Euclidean metric, the interior and closure of $A$ can be found: $$Int(A) = \{ (x,y) \in \RR^2 \mbox{ such that } -1 < x < 1, -1 < y < 1 \}.$$ $$Cl(A) = \{ (x,y) \in \RR^2 \mbox{ such that } -1 \leq x \leq 1, -1 \leq y \leq 1.$$