Talk:Utility maximization problem

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The attribution of the results to theorems is somewhat questionable.

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

The Weierstrass theorem

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]