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?
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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 $x$.
