Contour set in Mas-Collel, Winston and Green

Question

Mas-Colell, Winston and Green's Microeconomic Theory uses the notion of contour set, as shown hereunder:

In the context of Microeconomic Theory, what would be the definition of a contour set?

Answer 1

The upper contour set is $ UC(x)=\{ y|y \succsim x \} $, i.e., all the goods baskets that are at least as desirable as $x$. Similarly, the lower contour set is $LC(x)=\{ y|x \succsim y \} $, i.e., all the goods baskets that are at most as desirable as $x$.