Answer to Question #217027 in Differential Geometry | Topology for Prathibha Rose

Question

Give an example of a projection. Which is not closed

Answer 1

$\text{An example of this is;}\\\text{X = Y = $\mathbb{R,}$}\{(x,y)\text{ is a member of $\mathbb{R^2}$: xy=1 }\}$

$\text{We notice that the set is closed because it is a level set of the continous function}\\\text{f(x,y) = xy but its projection $\mathbb{R}/\{0\}$ is not closed as its complement$\{0\}$ is not open}$