Are These Regions in R^2 Compact?

[s_j_sawyer]

Homework Statement

Determine whether the following in R^2 are compact or not.

(i) [0,1] X [0,1)
(ii) [a,b] X [c,d] where a < b, c < d

The Attempt at a Solution

I have seen this notation before but I never knew what it meant.

 

[LeonhardEuler]

It means a rectangle. For instance if you call R^2 the x-y plane, then [0,1] X [0,1) would be the set of numbers where
0\leq x \leq 1
and
0\leq y &lt; 1

 

[gb7nash]

Draw a square in R² space with vertices at (0,0),(0,1),(1,0) and (1,1) and shade the box. The side edges and bottom edge are closed and the top edge is dotted. So any point on the top edge is not in the region [0,1] X [0,1).

Euler beat me. :(