Talk:Domain theory

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[edit] False claim under Important result

I deleted the following claim from the section on important results:

A poset D with a least element is a dcpo if and only if every monotone function f on D has a fixed point.

This is false. Condsider for example D = {0,1,2,3,..., x,y,z} where the naturals are ordered as 0 <= 1 <= 2 ... and x, y, z are three "infinities" (above naturals) with x <= z, y <= z and x, y incomparable. Then every monotone function on D has a fixed point, but D is not a dcpo. Frege 07:25, 27 March 2007 (UTC)