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The example using U = max(x,y} is not perfect substitutes. "Perfect substitutes have a linear utility function", according to the linked page. Ulaniantho ( talk) 05:22, 13 June 2022 (UTC) reply

The attribution of the results to theorems is somewhat questionable.

Charles Matthews 11:51, 26 Sep 2004 (UTC)

The Weierstrass theorem is: "Let X and Y be topological spaces. If f : X -> Y is continuous and X is compact, then Y is compact."

It is list in the Compact spaces page without any attribution. My microeconomics lecturer said it was called the Weierstrass theorem. It isn't given a name in any of my maths (Topology and Analysis) notes.

-- Clausen 05:52, 26 Sep 2004 (UTC)

The Weierstrass theorem is refering to the (Weierstrass) Extreme value theorem which states that a continuous function from a compact (non-empty) space to the real numbers attains a maximum and a minimum (see [1]). The Heine-Borel theorem is used in the proof of that theorem. Smmurphy^{( Talk)} 14:03, 23 August 2006 (UTC) reply