1
$\begingroup$

Mas-Collel, Winston and Green's Microeconomic Theory (3rd edition), states that the continuity of a preference relation implies the upper and lower contour sets of a bundle are closed. I would like to know why.

enter image description here

Definition of continuous preference relation:

enter image description here

Definition of open set:

enter image description here

Definition of closed set:

enter image description here

$\endgroup$

Browse other questions tagged or ask your own question.